ENGINEERING ENGINEERING ECONOMICS ECONOMICS SET 1 SET 1 SIMPLE INTEREST SIMPLE INTEREST 1.
1. FiFind thnd the inte intereerest onst on P6800.00 for 3 years at P6800.00 for 3 years at 11 % simple interest. 11 % simple interest. A Annss.. PP22,,224444..0000 2.
2. A maA man bon borrrrowoweded P10,000.00 from his P10,000.00 from his friend and arees to friend and arees to pay at the end of !0 pay at the end of !0 days "nder 8 % simple days "nder 8 % simple interest rate. #hat is interest rate. #hat is the re$"ired amo"nt the re$"ired amo"nt A
Annss.. PP1100,,220000..0000 3.
3. Annie Annie b"ys b"ys a tea tele&isle&isionion set from a mer'hant set from a mer'hant who o(ers P2),000.00 who o(ers P2),000.00 at the end of 60 days. at the end of 60 days. Annie wishes to pay Annie wishes to pay immediately and the immediately and the mer'hant o(ers to mer'hant o(ers to 'omp"te the
'omp"te the re$"iredre$"ired amo"nt on the amo"nt on the
ass"mption that money ass"mption that money is worth 14 % simple is worth 14 % simple interest. #hat is the interest. #hat is the re$"ired amo"nt re$"ired amo"nt A
Annss.. PP2244,,4422!!..!!** 4.
4. #hat #hat is is the the prinprin'ipal'ipal amo"nt if the amo"nt amo"nt if the amo"nt of interest at the end of of interest at the end of 2 + year is P4)00 2 + year is P4)00 for afor a
simple interest of 6 % per simple interest of 6 % per ann"m
ann"m A
Annss.. PP3300,,000000..0000
).
). ow low lon mon m"st a P"st a P40,40,000000 note bearin 4 %
note bearin 4 % simplesimple interest r"n to amo"nt to interest r"n to amo"nt to P41,3)0.00 P41,3)0.00 A Annss.. 33004 4 ddaayyss 6. 6. -f P1-f P16,000 6,000 earnearns P4s P480 in80 in ! months, what is the ! months, what is the ann"al rate of
ann"al rate of interestinterest A
Annss.. 4 4 %% *.
*. A tiA time dme depoeposit osit off P110,000 for 31 days P110,000 for 31 days earns P8!0.3! on earns P8!0.3! on mat"rity date after mat"rity date after ded"'tin the 20 % ded"'tin the 20 % withholdin ta on withholdin ta on interest in'ome. Find the interest in'ome. Find the rate of interest per rate of interest per ann"m.
ann"m. A
Annss.. 1111..**) ) %% 8.
8. A banA ban/ 'ha/ 'harres 12 %es 12 % simple interest on a simple interest on a P300.00 loan. ow m"'h P300.00 loan. ow m"'h will be repaid if the load will be repaid if the load is paid ba'/ in one l"mp is paid ba'/ in one l"mp s"m after three years. s"m after three years. A
Annss.. PP440088..0000 !.
!. A priA pri'e ta'e ta of P1 of P1200 i200 iss spe'ied if paid within 60 spe'ied if paid within 60 days b"t o(ers a 3 % days b"t o(ers a 3 % dis'o"nt for 'ash in 30 dis'o"nt for 'ash in 30
days. Find the rate of days. Find the rate of interest. interest. A Annss.. 33**..111 1 %% 10.-t is the pra'ti'e of 10.-t is the pra'ti'e of
almost all ban/ in the almost all ban/ in the Philippines that when Philippines that when they rant a loan, the they rant a loan, the interest for one year is interest for one year is a"tomati'ally ded"'ted a"tomati'ally ded"'ted from the prin'ipal from the prin'ipal amo"nt "pon release on amo"nt "pon release on money to a borrower. et money to a borrower. et "s therefore ass"me "s therefore ass"me that yo" applied for a that yo" applied for a loan with a ban/ and the loan with a ban/ and the P80000 was appro&ed at P80000 was appro&ed at an interest rate of 14 % an interest rate of 14 % of whi'h P11200 was of whi'h P11200 was ded"'ted and yo" were ded"'ted and yo" were i&en a 'he'/ of i&en a 'he'/ of
P68800. in'e yo" ha&e P68800. in'e yo" ha&e to pay the amo"nt of to pay the amo"nt of P80000 one year after, P80000 one year after, what then will be the what then will be the e(e'ti&e interest rate e(e'ti&e interest rate A
Annss.. 1166..228 8 %% 11.r. . de la 5r" 11.r. . de la 5r"
borrowed money from a borrowed money from a ban/. e re'ei&ed from ban/. e re'ei&ed from the ban/ P1,340.00 and the ban/ P1,340.00 and promised to pay promised to pay P1,)00.00 at the end of P1,)00.00 at the end of ! months. 7etermine ! months. 7etermine the simple interest rate the simple interest rate and the 'orrespondin and the 'orrespondin dis'o"nt rate or often dis'o"nt rate or often
referred to as the referred to as the 9an/ers dis'o"nt:. 9an/ers dis'o"nt:. Ans. Ans. 1).!2 1).!2 % % ;; 13.*3 % 13.*3 % 12.A man
12.A man borroweborrowed from ad from a ban/ "nder a promissory ban/ "nder a promissory note that he sined in note that he sined in the amo"nt pf
the amo"nt pf
P2),000.00 for a period P2),000.00 for a period of one year. e re'ei&ed of one year. e re'ei&ed only the amo"nt of only the amo"nt of P21,!1).00 after the P21,!1).00 after the ban/ 'olle'ted the ban/ 'olle'ted the ad&an'e interest and an ad&an'e interest and an additional amo"nt of additional amo"nt of P8).00 for notarial and P8).00 for notarial and inspe'tion fees. #hat inspe'tion fees. #hat was the rate of
was the rate of interestinterest that the ban/ 'olle'ted that the ban/ 'olle'ted in ad&an'e
in ad&an'e A
Annss.. 1133..664 4 %% 13.Anes Abanilla was 13.Anes Abanilla was
ranted a loan of ranted a loan of P20,000 by her P20,000 by her employer 5P -nd"strial employer 5P -nd"strial Fabri'ator and Fabri'ator and 5onstr"'tion 5orporation 5onstr"'tion 5orporation with an interest at 6 % with an interest at 6 % for 180 days on the for 180 days on the prin'ipal 'olle'ted in prin'ipal 'olle'ted in ad&an'e. <he ad&an'e. <he 'orporation wo"ld 'orporation wo"ld a''ept a promissory a''ept a promissory note for P20,000 non = note for P20,000 non = interest for 180 days. -f interest for 180 days. -f dis'o"nted at on'e, nd dis'o"nted at on'e, nd
the pro'eeds on the the pro'eeds on the note.
note. A
Annss.. PP1188,,880000 14.P4000 is
14.P4000 is borroweborrowed ford for *) days at 16 % per *) days at 16 % per ann"m simple interest. ann"m simple interest. ow m"'h will be d"e ow m"'h will be d"e at the end of *) days at the end of *) days A Annss.. PP44113333..3333 1).r. Almaro made a 1).r. Almaro made a money mar/et money mar/et pla'ement of pla'ement of P1,000,000 for 30 days P1,000,000 for 30 days at *.) % per year. -f the at *.) % per year. -f the withholdin ta is 20 %, withholdin ta is 20 %, what is the net
what is the net interestinterest that r. Almaro will that r. Almaro will re'ei&e at the end of re'ei&e at the end of the month the month A Annss.. PP))000000 ENGINEERING ENGINEERING ECONOMICS ECONOMICS SET 2 SET 2
16.A bill for motorboat 16.A bill for motorboat spe'ies the 'ost as spe'ies the 'ost as P1200 d"e at the end P1200 d"e at the end of 100 days b"t o(ers a of 100 days b"t o(ers a 4 % dis'o"nt for 'ash in 4 % dis'o"nt for 'ash in 30 days. #hat is the 30 days. #hat is the hihest rate, simple hihest rate, simple interest at whi'h the interest at whi'h the
b"yer 'an a(ord to b"yer 'an a(ord to borrow money in order to borrow money in order to ta/e ad&antae of the ta/e ad&antae of the dis'o"nt dis'o"nt A Annss.. 2211..4 4 %% 1*.-n b"yin a 'omp"ter 1*.-n b"yin a 'omp"ter
dis/, the b"yer was dis/, the b"yer was o(ered the options of o(ered the options of payin P2)0 'ash at the payin P2)0 'ash at the end of 30 days or P2*0 at end of 30 days or P2*0 at the end of 120 days. At the end of 120 days. At what rate is the b"yer what rate is the b"yer payin simple interest if payin simple interest if he aree to pay at the he aree to pay at the end of 120 days. end of 120 days. A
Annss.. 332 2 %%
18.Find the dis'o"nt if P2000 18.Find the dis'o"nt if P2000
is dis'o"nted for 6 is dis'o"nted for 6 months at 8 % simple months at 8 % simple dis'o"nts. dis'o"nts. A Annss.. PP8800..0000 1!.5omp"te the dis'o"nt if 1!.5omp"te the dis'o"nt if P2000 is dis'o"nted for 6 P2000 is dis'o"nted for 6 months at 8 % simple months at 8 % simple interest. interest. A Annss.. PP**66..!!22 20.>n ar'h 1, 20.>n ar'h 1, 1!!6 r.1!!6 r. Almaro obtains a loan of Almaro obtains a loan of P1)00 from r. Abella P1)00 from r. Abella and sins a note and sins a note promisin to pay the promisin to pay the prin'ipal and
prin'ipal and a''"m"lated simple a''"m"lated simple interest at the rate of ) % interest at the rate of ) % at the end of 120 days. at the end of 120 days.
>n ay 1),
>n ay 1), 1!!6, r.1!!6, r. Abella dis'o"nts the Abella dis'o"nts the note at the ban/ note at the ban/ whosewhose dis'o"nt rate is 6 %. dis'o"nt rate is 6 %. #hat does he re'ei&ed #hat does he re'ei&ed A
Annss.. PP11))1133..))66 21.A deposit of P110,000 21.A deposit of P110,000 was made for 31 days. was made for 31 days. <he net inter
<he net interest afterest after ded"'tin 20 % ded"'tin 20 % withholdin ta is withholdin ta is P8!0.36. Find the rate of P8!0.36. Find the rate of ret"rn ann"ally.
ret"rn ann"ally. A
Annss.. 1111..**) ) %% 22.-f yo"
22.-f yo" borrowed moneyborrowed money from yo"r friend with from yo"r friend with simple interest of 12 %, simple interest of 12 %, nd the present worth of nd the present worth of P)0,000 whi'h is d"e at P)0,000 whi'h is d"e at the end of * months. the end of * months. A
Annss.. PP4466,,**2288..!!** 23.-f the
23.-f the 'ompo"nd interest'ompo"nd interest on P3,000.00 in 2 years on P3,000.00 in 2 years is P)00.00, then the is P)00.00, then the 'ompo"nd interest on 'ompo"nd interest on P3,000.00 in 4 years is? P3,000.00 in 4 years is? A Annss.. PP11,,008833..0000 24.A man
24.A man borrowborrowed P2000ed P2000 from a ban/ and promise from a ban/ and promise to pay the amo"nt for to pay the amo"nt for one year. e re'ei&ed one year. e re'ei&ed only the amo"nt of only the amo"nt of P1,!20 after the ban/ P1,!20 after the ban/ 'olle'ted an ad&an'e 'olle'ted an ad&an'e interest of P80. #hat interest of P80. #hat
was the rate of
was the rate of dis'o"ntdis'o"nt and the rate of
and the rate of interestinterest that the ban/ 'olle'ted that the ban/ 'olle'ted in ad&an'e. in ad&an'e. A Annss.. 4 4 % % ; ; 44..11* * %% COMPOUND INTEREST COMPOUND INTEREST 2).A''"m"late P),000.00 2).A''"m"late P),000.00 for 10 years at 8 % for 10 years at 8 % 'ompo"nded $"arterly. 'ompo"nded $"arterly. A Annss.. PP1111,,004400..2200 26.A''"m"late P),000.00 26.A''"m"late P),000.00 for 10 years at 8 % for 10 years at 8 % 'ompo"nded semi = 'ompo"nded semi = ann"ally. ann"ally. A Annss.. PP1100,,!!))))..6611 2*.A''"m"late P),000.00 2*.A''"m"late P),000.00 for 10 years at 8 % for 10 years at 8 % 'ompo"nded monthly. 'ompo"nded monthly. A Annss.. PP1111,,00!!88..2200 28.A''"m"lates P),000.00 28.A''"m"lates P),000.00 for 10 years at 8 % for 10 years at 8 % 'ompo"nded ann"ally. 'ompo"nded ann"ally. A Annss.. PP1100,,**!!44..6622 2!.ow lon will it ta/e 2!.ow lon will it ta/e P1,000 to amo"nt to P1,000 to amo"nt to P1,346 if in&ested at 6 % P1,346 if in&ested at 6 % 'ompo"nded $"arterly 'ompo"nded $"arterly A Annss.. ) ) yyeeaarrss 30.ow lon will it ta/e for 30.ow lon will it ta/e for an in&estment to do"ble an in&estment to do"ble its amo"nt if in&ested at its amo"nt if in&ested at an interest rate of 6 % an interest rate of 6 % 'ompo"nded bi = 'ompo"nded bi = monthly monthly A Annss.. 112 2 yyeeaarrss
31.-f yo"
31.-f yo" borrowborroweded P10,000 from a ban/ P10,000 from a ban/ with 18 %
with 18 % interest perinterest per ann"m, what is the ann"m, what is the total amo"nt to be total amo"nt to be repaid at the end of repaid at the end of one year
one year A
Annss.. PP1111,,880000..0000 32.#hat is the e(e'ti&e 32.#hat is the e(e'ti&e
rate for an interest rate rate for an interest rate of 12 % of 12 % 'ompo"nded'ompo"nded 'ontin"o"sly 'ontin"o"sly A Annss.. 1122..**) ) %% 33.ow lon will it ta/e for 33.ow lon will it ta/e for
an in&estment to an in&estment to &efold its amo"nt if &efold its amo"nt if money is worth 14 % money is worth 14 % 'ompo"nded semi = 'ompo"nded semi = ann"ally ann"ally A Annss.. 1122
34.An interest rate of 8 % 34.An interest rate of 8 %
'ompo"nded semi = 'ompo"nded semi = ann"ally is how many ann"ally is how many per'ent if 'ompo"nded per'ent if 'ompo"nded $"arterly $"arterly A Annss.. **..!!2 2 %% 3).A man is
3).A man is epe'tin toepe'tin to re'ei&e P4)0,000.00 at re'ei&e P4)0,000.00 at the end of * years. -f the end of * years. -f money is worth 14 % money is worth 14 % 'ompo"nded $"arterly, 'ompo"nded $"arterly, how m"'h is it worth at how m"'h is it worth at present present A Annss.. PP11**11,,**4444..44)) ENGINEERING ENGINEERING ECONOMICS ECONOMICS SET 3 SET 3
36.A man has a will of 36.A man has a will of
P6)0,000.00 from his P6)0,000.00 from his father. -f his father father. -f his father deposited an amo"nt of deposited an amo"nt of P4)0,000.00 in a tr"st P4)0,000.00 in a tr"st f"nd earnin 8 % f"nd earnin 8 % 'ompo"nded ann"ally, 'ompo"nded ann"ally, after how many years will after how many years will the man re'ei&e his will the man re'ei&e his will A Annss.. 44..**8 8 yyeeaarrss 3*.r. Adam deposited 3*.r. Adam deposited P120,000.00 in a ban/ P120,000.00 in a ban/ who o(ers 8 % interest who o(ers 8 % interest 'ompo"nded $"arterly. -f 'ompo"nded $"arterly. -f the interest is s"b@e't to a the interest is s"b@e't to a 14 % ta, how m"'h will 14 % ta, how m"'h will he re'ei&e after ) years he re'ei&e after ) years A Annss.. PP11**00,,1144!!..**** 38.#hat interest 38.#hat interest 'ompo"nded monthly is 'ompo"nded monthly is e$"i&alent to an interest e$"i&alent to an interest rate of 14 % 'ompo"nded rate of 14 % 'ompo"nded $"arterly $"arterly A Annss.. 1133..884 4 %%
3!.#hat is the present worth 3!.#hat is the present worth of two P100.00 payments of two P100.00 payments at the end of the third at the end of the third and the fo"rth year <he and the fo"rth year <he
ann"al interest rate is 8 ann"al interest rate is 8 %.
%. A
Annss.. PP11))22..88** 40.A rm
40.A rm borrowborrows P2000.00s P2000.00 for 6 years at 8 %. for 6 years at 8 %. AtAt the end of 6 years, it the end of 6 years, it renews the loan for the renews the loan for the amo"nt d"e pl"s P2000 amo"nt d"e pl"s P2000 more for 2 years at 8 %. more for 2 years at 8 %. #hat is the l"mp s"m #hat is the l"mp s"m d"e. d"e. A Annss.. PP66,,003344..6666 41.At an ann"al rate of 41.At an ann"al rate of ret"rn of 8 %, what is ret"rn of 8 %, what is the f"t"re worth of the f"t"re worth of P1000 at the end of 4 P1000 at the end of 4 years years A Annss.. PP11336600..))00 42.A st"dent has money 42.A st"dent has money
i&en by his
i&en by his randfatherrandfather in the amo"nt of
in the amo"nt of P20,000.00. ow m"'h P20,000.00. ow m"'h money in the form of money in the form of interest will he et if the interest will he et if the money is p"t in a ban/ money is p"t in a ban/ that o(ers 8 % rate that o(ers 8 % rate 'ompo"nded ann"ally, 'ompo"nded ann"ally, at the end of * years at the end of * years A
Annss.. PP3344,,22**66..4488 43.-f the interest rate on an 43.-f the interest rate on an
a''o"nt is 11.) % a''o"nt is 11.) % 'ompo"nded yearly, 'ompo"nded yearly, approim
approimately ately howhow many years will it many years will it ta/eta/e to triple the amo"nt to triple the amo"nt
A
Annss.. 110 0 yyeeaarrss 44.<he nominal interest 44.<he nominal interest
rate is 4 %. ow m"'h is rate is 4 %. ow m"'h is my P10,000.00 worth in my P10,000.00 worth in 10 years in a 10 years in a 'ontin"o"sly 'ontin"o"sly 'ompo"nded a''o"nt 'ompo"nded a''o"nt A Annss.. PP1144,,!!1188..22)) 4).ow m"'h m"st be 4).ow m"'h m"st be in&ested on an"ary 1, in&ested on an"ary 1, year 1 in order to year 1 in order to a''"m"late P2,000.00 a''"m"late P2,000.00 on an"ary 1, year 6 at 6 on an"ary 1, year 6 at 6 %. %. A Annss.. PP11,,44!!))..0000 46.-f P)000.00 shall 46.-f P)000.00 shall
a''"m"late for 10 years a''"m"late for 10 years at 8 %
at 8 % 'ompo"nded'ompo"nded $"arterly. Find the $"arterly. Find the 'ompo"nded interest at 'ompo"nded interest at the end of 10 years. the end of 10 years. A Annss.. PP66,,004400..2200 4*.<he amo"nt of 4*.<he amo"nt of P1,)00.00 was deposited P1,)00.00 was deposited in a ban/ a''o"nt, 20 in a ban/ a''o"nt, 20 years ao. <oday is years ao. <oday is worth P3,000.00. worth P3,000.00. -nterest is paid semi = -nterest is paid semi = ann"ally. 7etermine the ann"ally. 7etermine the interest rate paid on this interest rate paid on this a''o"nt
a''o"nt A
Annss.. 33..) ) %% 48.-f the nominal
48.-f the nominal interestinterest rate is 3 %, how m"'h is rate is 3 %, how m"'h is P), 000.00 worth in 10 P), 000.00 worth in 10
years in a 'ontin"o"sly 'ompo"nded a''o"nt Ans. P6,*)0.00 4!.A mer'hant p"ts in his
P2,000.00 to a small b"siness for a period of si years. #ith a i&en interest rate on the in&estment of 1) % per year, 'ompo"nded ann"ally, how m"'h will he 'olle't at the end of the sith year
Ans. P4,626.00 )0.A person in&ests
P4,)00.00 to be 'olle'ted in 8 years. i&en that the interest rate on the in&estment is 14.) % per year 'ompo"nded ann"ally, what s"m will be 'olle'ted in 8 years Ans. P13,2!4.02 )1.-n year ero, yo" in&est
P10,000.00 in a 1) % se'"rity for ) years. 7"rin that time, the a&erae ann"al inBation is 6 %. ow m"'h, in terms of year ero pesos, will be in the a''o"nt at the mat"rity
Ans. P1),030.00
)2.A 'ompany in&ests P10,000.00 today to be repaid in &e years in one l"mp s"m at 12 %
'ompo"nded ann"ally. -f the rate of inBation is 3 % 'ompo"nded ann"ally, how m"'h prot in present day pesos is realied o&er &e years Ans. P),202.00 )3.5omp"te the e(e'ti&e
rate for an interest rate of 16 % 'ompo"nded
ann"ally. Ans. 16 % )4.5omp"te the e(e'ti&e
rate for an interest rate of 16 % 'ompo"nded $"arterly. Ans. 16.!8 % ENGINEERING ECONOMICS SET 4 )).5on&ert 12 % 'ompo"nded semi = ann"ally to % 'ompo"nded $"arterly. Ans. 11.83 % )6.5on&ert 12 % 'ompo"nded semi = ann"ally to % 'ompo"nded monthly. Ans. 11.*1 % )*.A ban/ is ad&ertisin !.)
% a''o"nts that yield !.84 % ann"ally. ow often is the interest 'ompo"nded aC 7aily bC onthly 'C 9i = monthly dC D"arterly Ans. $"arterly )8.9y the 'onditions of a
will, the s"m of P2),000.00 is left to a irl to be held in a tr"st f"nd by her "ardian "ntil it amo"nt to P4), 000.00. #hen will the irl re'ei&e the money if the f"nd is in&ested at 8 % 'ompo"nded
$"arterly
Ans. *.42 years )!.#hat is the e(e'ti&e
rate 'orrespondin to 16 % 'ompo"nded daily <a/e 1 year E 360 days.
Ans. 1*.3) % 60.A man epe'ts to
re'ei&e P20,000.00 in 10 years. ow m"'h is that money worth now
'onsiderin interest at 6 % 'ompo"nded
$"arterly
Ans. P11,02).2) 61.#hat amo"nt will be
a''"m"lated by a present in&estment of P1*,200 in 6 years at 2 % 'ompo"nded $"arterly Ans. P1!,38*.1) 62.#hat rate of interest
'ompo"nded ann"ally m"st be re'ei&ed if an in&estment of
P)4,000.00 made now will res"lt in a re'eipt of P*2,000.00 ) years hen'e Ans. ).!2 % 63.#ith interest at 6 % 'ompo"nded ann"ally, how m"'h is re$"ired * years hen'e to repay an P8 loan made today Ans. P12,02!,042 64.-f money is worth 6 %
'ompo"nded ann"ally, what payment 12 years from now is e$"i&alent to a payment of P*,000.00 ! years from now
6).-f money is worth 6 % 'ompo"nded ann"ally, how m"'h 'an be loaned now if P6,000.00 will be repaid at the end of 8 years. Ans. P3,*64.)0 66.A person in&est P4,)00
to be 'olle'ted in 8 years. i&en that the interest rate on the in&estment is 14.) % per year, 'ompo"nded ann"ally, what s"m, in pesos, will be 'olle'ted eiht years hen'e Ans. P13,2!4.00 6*.-f P)00,000 is deposited at a rate of 11.2) % 'ompo"nded monthly, determine the 'ompo"nded interest after * years and ! months. Ans. 6!0,84! 68.P200,000 was deposited on an"ary 1, 1!88 at an interest rate of 24 % 'ompo"nded semi = ann"ally. ow m"'h wo"ld the s"m on an"ary 1, 1!!3
Ans. P621,1*0.00 6!.Find the nominal rate
that if 'on&erted $"arterly 'o"ld be "sed
instead for 1) % 'ompo"nded semi = ann"ally
Ans. 14.*3 % *0.#hi'h of the followin
has the least e(e'ti&e ann"al interest rate aC 12 % 'ompo"nded $"arterly bC 11.) % 'ompo"nded monthly 'C 11.* % 'ompo"nded semi = ann"ally dC 12.2 % 'ompo"nded ann"ally Ans. 11.* % 'ompo"nded semi ann"ally
*1.>ne h"ndred tho"sand pesos was pla'ed in a time deposit that earns ! % 'ompo"nded $"arterly, ta free. After how many years wo"ld it be able to earn a total interest of fty tho"sand pesos Ans. 4.)6
*2.<he amo"nt of P2,82).00 in 8 years at ) %
'ompo"nded $"arterly is? Ans. P4,203.!* *3.<he amo"nt of P2,82).00 in 8 years at ) % 'ompo"nded 'ontin"o"sly is? Ans. P4,214.40 *4.<he amo"nt of P12,800 in 4 years at ) % 'ompo"nded $"arterly is ? Ans. P1,)614.)! ENGINEERING ECONOMICS SET 5 *).#hat rate G%C 'ompo"nded $"arterly is e$"i&alent to 6 % 'ompo"nded semi = ann"ally Ans. ).!6 % *6.Fifteen per'ent G1) %C
when 'ompo"nded semi = ann"ally will ha&e e(e'ti&e rate of ? Ans. 1).)6 % **.#hat rate of interest
'ompo"nded ann"ally is the same as the rate of interest of 8 %
'ompo"nded $"arterly Ans. 8.24 % *8.ow lon will it ta/e the
money to triple itself if in&ested at 10 % 'ompo"nded semi = ann"ally
Ans. 11.3 years *!.#hat is the a''"m"lated
amo"nt after three G3C
years of P6,)00.00 in&ested at the rate of 12 % per year
'ompo"nded semi = ann"ally
Ans. P!,221.00 80.#hat interest rate,
'ompo"nded monthly is e$"i&alent to 10 % e(e'ti&e rate Ans. !.)* % 81.A man wishes his son to
re'ei&e P)00,000.00 ten years from now. #hat amo"nt sho"ld he in&est now if it will earn
interest of 12 % 'ompo"nded ann"ally d"rin the rst ) years and 1) % 'ompo"nded $"arterly d"rin the net ) years
Ans. P12!,8)3.48 82.A sa&ins asso'iation
pays 4 % interest $"arterly. #hat is the e(e'ti&e ann"al interest rate
Ans. 16.!8) % 83.A ban/ o(ers 1.2 %
e(e'ti&e monthly interest. #hat is the e(e'ti&e ann"al rate with monthly
'ompo"ndin Ans. 1).4 %
84.#hat is the present worth of P2*,000.00 d"e in 6 years if money is worth 13 % and is 'ompo"nded semi = ann"ally Ans. P12,681.00 8).<he amo"nt of P12, 800 in 4 years at ) % 'ompo"nded $"arterly is ? Ans. P1),614.)! 86.A man borrows money
from a ban/ whi'h "ses a simple dis'o"nt rate of 14 %. e sins a promissory note promisin to pay P)00.00 per month at the end of 4th, 6th and *th months respe'ti&ely. 7etermine the amo"nt of money that he re'ei&ed from the ban/. Ans. P1,403.68 8*.A nominal interest of 3
% 'ompo"nded 'ontin"o"sly is i&en on the a''o"nt. #hat is the a''"m"lated amo"nt of P10,000 after 10 years Ans. P13,4!8.60 88.9y the 'ondition of a
will, the s"m of P2,000 is left to a irl to be
held in tr"st f"nd by her "ardian "ntil it amo"nts to P)0,000.00. #hen will the irl re'ei&e the money if the f"nd is in&ested at 8 %
'ompo"nded $"arterly Ans. 11.)* years 8!.A man epe'ts to re'ei&e
P2),000 in 8 years. ow m"'h is that worth now 'onsiderin interest at 8 % 'ompo"nded $"arterly Ans. P13,26).83 !0.P)00,000 was deposited at an interest of 6 % 'ompo"nded $"arterly. 5omp"te the 'ompo"nd interest after 4 years and ! months.
Ans. P163,4*).3* !1.-f the nominal interest rate is 3 %, how m"'h is P),000 in 10 years in a 'ontin"o"sly 'ompo"nded a''o"nt Ans. P6,*)0 !2.P200,000 was deposited
for a period of 4 years and 6 months and bears on interest of P8),64!.2). what is the rate of
interest if it is
'ompo"nded $"arterly
Ans. 8 % !3.ow many years will
P100,00 earned a 'ompo"nd interest rate is ! % 'ompo"nded $"arterly
Ans. 4.)) years !4.A 'ertain amo"nt was
deposited ) years and ! months ao at an interest of 8 %
'ompo"nded $"arterly. -f the s"m mow is
P31),3*!.8), how m"'h was the amo"nt
deposited
Ans. P200,000 ENGINEERING ECONOMICS SET 6
!).-f the rate of interest is 12 % 'ompo"nded ann"ally , nd the e$"i&alent rate of interest if it is 'ompo"nded $"arterly. Ans. 11.4! % !6.ow lon will it ta/e
money to do"ble itself if in&ested at ) %
'ompo"nded ann"ally Ans. 14 years !*.5omp"te the e(e'ti&e
ann"al interest rate
whi'h is e$"i&alent to ) % nominal ann"al interest 'ompo"nded 'ontin"o"sly.
Ans. ).13 % !8.5omp"te the nominal
interest rate of a 'ontin"o"sly
'ompo"nded loan if the e(e'ti&e interest rate is 2) %
Ans. loge 1.2) !!.A man wishes to ha&e
P40,000 in a 'ertain f"nd at the end of 8 years. ow m"'h sho"ld be in&est in a f"nd that will pay 6 % 'ompo"nded 'ontin"o"sly Ans. P24.*)1.34 100. -f the e(e'ti&e
ann"al interest rate in 4 %, 'omp"te the e$"i&alent nominal ann"al interest 'ompo"nded 'ontin"o"sly. Ans. 3.!2 % 101. #hat is the nominal
rate of interest 'ompo"nded 'ontin"o"sly for 10 years if the 'ompo"nd
amo"nt fa'tor is e$"al to 1.34!86
Ans. 3 % 102. Ameri'an Hpress
5orp. 'hares 1 + % interest per month, 'ompo"nded 'ontin"o"sly on the "npaid balan'e
p"r'hases made on this 'redit 'ard. 5omp"te the e(e'ti&e rate of interest. Ans. 1!.*2 % 103. -f the nominal interest is 12 % 'ompo"nded 'ontin"o"sly, 'omp"te the e(e'ti&e ann"al rate of interest. Ans. 12.*) % 104. 5omp"te the
di(eren'e in the f"t"re amo"nt of P)00 'ompo"nded ann"ally at nominal rate of ) % and if it is 'ompo"nded 'ontin"o"sly for ) years at the same rate. Ans. P3.8* 10). -f the e(e'ti&e
interest rate is 24 %, what nominal rate of interest is 'hared for a
'ontin"o"sly 'ompo"nded loan Ans. 21.)1 % 106. #hat is the nominal
rate of interest 'ompo"nded
'ontin"o"sly for 8 years if the present worth fa'tor is e$"al to 0.618*83) Ans. 6 %
10*. #hat is the di(eren'e of the amo"nt 3 years from now for a 10 % simple interest and 10 % 'ompo"nd interest per year
Ans. P1))
108. Find the dis'o"nt if P2,000 is dis'o"nted for 6 months at 8 % 'ompo"nd $"arterly.
Ans. P**.66 10!. -f a s"m of money
triples in a 'ertain period of time at a i&en rate of interest, 'omp"te the &al"e of the sinle payment present worth fa'tor.
Ans. 0.333
110. -f the sinle payment amo"nt fa'tor for a period of ) years is 1.33822. #hat is the nearest &al"e of the interest rate
Ans. 6 %
111. -f the sinle payment present worth fa'tor for a period of 8 years is e$"al to 0.)8201, 'omp"te the nearest &al"e of the rate of interest for that period. Ans. * %
112. -f money is worth 8 % 'ompo"nded $"arterly, 'omp"te the sinle payment amo"nt fa'tor for a period of 6 years. Ans. 1.60844 113. A s"m of P1,000.00 is
in&ested now and left for 8 years, at whi'h time the prin'ipal is
withdrawn. <he interest has a a''r"ed is left for another 8 years. -f the e(e'ti&e ann"al interest rate is ) %, what will be the withdrawn amo"nt at the end of the 16th year
Ans. P*0).42 114. P)00,000 was
deposited 20.1) years ao at an interest rate of * % 'ompo"nded semi = ann"ally. ow m"'h is the s"m now Ans. P2,000,000 11). ow m"'h sho"ld yo" p"t into a 10 % sa&ins a''o"nt in order to ha&e P10,000.00 in &e years
Ans. P6,210.00
FLUID MECHANICS and HYDRAULICS SET 1 PROPERTIES OF FLUIDS 1. A reser&oir of ly'erin has a mass of 120 / and a &ol"me of 0.!)2 m3. Find its weiht, mass density, spe'i' weiht and spe'i' ra&ity.
Ans. 11.** /I, 1261 /Jm3, 12.36 /IJm3, 1.26 2. <he spe'i' ra&ity of
oil is 0.82. 5al'"late its spe'i' weiht in lbJft3 and /IJm3 and mass density in sl"sJft3 and /Jm3.
Ans. )1.1* lbJft3, 8.04 /IJm3, 1.)! sl"sJft3 and 820 /Jm3. 3. A body re$"ires a for'e
at a rate of 0.20 mJs at a rate of 0.20 mJs22.. 7etermine the mass of 7etermine the mass of the body in / and in the body in / and in sl"s. sl"s. Ans. Ans. )00 )00 /, /, 34.334.3 sl"s sl"s 4.
4. <he <he weiht weiht of of aa body is 100 lb. body is 100 lb.
7etermine its weiht in 7etermine its weiht in Iewtons, and its Iewtons, and its a''eleration if a net a''eleration if a net for'e of )0 lb is applied for'e of )0 lb is applied to the body. to the body. Ans. Ans. 444.8 444.8 I, I, 16.0!16.0! ftJs ftJs22, , 4.!0 4.!0 mJsmJs22 ).
). A litA liter of er of watewater weir weihshs abo"t !.*) I. 5omp"te abo"t !.*) I. 5omp"te its mass in /ilorams. its mass in /ilorams. Ans.
Ans. 0.!!4 0.!!4 // 6.
6. <he <he spe'i' spe'i' ra&ity ra&ity ofof ethyl al'ohol is 0.*!. ethyl al'ohol is 0.*!. 5al'"late its spe'i' 5al'"late its spe'i' weiht in /IJm weiht in /IJm33 and and mass density in /Jm mass density in /Jm33..
Ans.
Ans. *.*3 *.*3 /IJm/IJm33,, *!0 /Jm
*!0 /Jm33 *.
*. A $A $"art "art of of waterwater weihs 2.08 lb. weihs 2.08 lb. 5omp"te its mass in 5omp"te its mass in sl"s and /ilorams. sl"s and /ilorams. Ans. Ans. 0.006460.00646 sl"s, 0.!43 / sl"s, 0.!43 / 8.
8. -f -f an an ob@e't ob@e't has has aa mass of 22 / at sea mass of 22 / at sea le&el. aC #hat will be its le&el. aC #hat will be its
weiht at a point where weiht at a point where the a''eleration d"e to the a''eleration d"e to ra&ity E !.*) mJs ra&ity E !.*) mJs22 bC bC #hat will be its mass at #hat will be its mass at that point
that point Ans.
Ans. 214.) 214.) I, I, 22 22 // !.
!. >ne '"bi' >ne '"bi' foot offoot of ly'erine has a mass of ly'erine has a mass of 2.44 sl"s. Find its 2.44 sl"s. Find its spe'i' weiht in lbJft spe'i' weiht in lbJft33 and /IJm and /IJm33.. Ans. Ans. *8.6 *8.6 lbJftlbJft33, 12.3), 12.3) /IJm /IJm33
10. <he &ol"me of a ro'/ is 10. <he &ol"me of a ro'/ is fo"nd to be 0.0001) m fo"nd to be 0.0001) m33.. -f the ro'/s sp. r. is 2.6, -f the ro'/s sp. r. is 2.6, what is the weiht in what is the weiht in Iewtons
Iewtons Ans.
Ans. 3.82 3.82 II 11. A 'ertain
11. A 'ertain asoline weihsasoline weihs 46.) lbJft
46.) lbJft33. #hat are its. #hat are its mass density, spe'i' mass density, spe'i' &ol"me and spe'i' &ol"me and spe'i' ra&ity ra&ity Ans. Ans. 1.44 1.44 sl"sJftsl"sJft33,, 0.6!4 ft 0.6!4 ft33Jsl"s, 0.*42Jsl"s, 0.*42 12. -f the spe'i' &ol"me of 12. -f the spe'i' &ol"me of
a
a 'ertain 'ertain as as is is 0.*8480.*848 m
m33J/, what is its spe'i'J/, what is its spe'i' weiht
weiht Ans.
Ans. 12.) 12.) II 13.
13. -f the spe'-f the spe'i' weiht ofi' weiht of the s"bstan'e is 8.2 the s"bstan'e is 8.2 /IJm
/IJm33, what is its mass, what is its mass density
density Ans.
Ans. 836 836 /Jm/Jm33
14.An ob@e't at a 'ertain 14.An ob@e't at a 'ertain lo'ation has a mass of lo'ation has a mass of 2.0 / and weihs 1!.0 2.0 / and weihs 1!.0 I on a sprin balan'e. I on a sprin balan'e. #hat is the a''eleration #hat is the a''eleration d"e to ra&ity at this d"e to ra&ity at this lo'ation
lo'ation Ans.
Ans. !.)0 !.)0 mJsmJs22 1).
1). -f -f an an ob@e't ob@e't has has aa mass of 2.0 sl"s at sea mass of 2.0 sl"s at sea le&el, what wo"ld be its le&el, what wo"ld be its mass be at a lo'ation mass be at a lo'ation where the a''eleration where the a''eleration d"e to ra&ity is 30.00 d"e to ra&ity is 30.00 ftJs ftJs22 Ans. Ans. 2.0 2.0 sl"ssl"s 16.
16. #hat wo#hat wo"ld be "ld be thethe weiht of a 3 / mass on weiht of a 3 / mass on a planet where the a planet where the a''eleration d"e to a''eleration d"e to ra&ity is 10.00 mJs ra&ity is 10.00 mJs22 Ans. Ans. 30.00 30.00 II 1*.
1*. 7etermine 7etermine the weithe weihtht of a )sl" bo"lder at a of a )sl" bo"lder at a pla'e where the pla'e where the a''eleration d"e to a''eleration d"e to ra&ity is 31.* ftJs ra&ity is 31.* ftJs22.. Ans. Ans. 1)8 1)8 lblb 18.
18. -f -f 200 200 ftft33 of oil weihs of oil weihs 10)20 lb, 'al'"late its 10)20 lb, 'al'"late its spe'i' weiht, density spe'i' weiht, density and spe'i' ra&ity. and spe'i' ra&ity.
Ans.
Ans. )2.6 )2.6 lbJftlbJft33, 1.63, 1.63 sl"sJft
sl"sJft33, 0.843, 0.843 1!.
1!. Find Find the the heiht heiht of of thethe free s"rfa'e if 0.8 ft free s"rfa'e if 0.8 ft33 of of
water is po"red into a water is po"red into a 'oni'al tan/ 20 in hih 'oni'al tan/ 20 in hih with a base radi"s of 10 with a base radi"s of 10 in. ow m"'h additional in. ow m"'h additional water is re$"ired to ll water is re$"ired to ll the tan/ the tan/ Ans. *13 Ans. *13 inin33 20.
20. A A 'oni'al 'oni'al tan/ tan/ 20 20 inin hih and a base hih and a base radi"sradi"s 10 in., holds 30.) / of 10 in., holds 30.) / of salad oil, what is the salad oil, what is the density of the oil density of the oil
Ans.
Ans. 88! 88! /Jm/Jm33 UNIT WEIGHT OF AIR UNIT WEIGHT OF AIR AND GASES AND GASES 21.
21. #hat is #hat is the spe'i'the spe'i' weiht of air at weiht of air at 480 /Pa absol"te 480 /Pa absol"te and 21 and 21oo55 Ans.
Ans. )).81 )).81 IJmIJm33 22.
22. A as A as at 20at 20oo5 and 0.215 and 0.21 pa abs has a &ol"me of pa abs has a &ol"me of 41 and a as 'onstant 41 and a as 'onstant K of 210 ImJ/L. K of 210 ImJ/L. 7etermine the density 7etermine the density and mass of the as. and mass of the as.
Ans.
Ans. 3.41 3.41 /Jm/Jm33,, 0.140 /
0.140 /
23. Find the mass density of 23. Find the mass density of
heli"m at a
heli"m at a temperat"rtemperat"ree of 4
of 4oo5 and a press"re of5 and a press"re of 184 /Pa ae, if
184 /Pa ae, if
atmospheri' press"re is atmospheri' press"re is
101.!2 /Pa. K E 20*! 101.!2 /Pa. K E 20*! J/ L. J/ L. Ans. Ans. 0.4!6) 0.4!6) /Jm/Jm33 24.
24. 5al'"late the5al'"late the density of water &apor density of water &apor at 3)0 /Pa abs and at 3)0 /Pa abs and 20
20oo5 if its as 'onstant5 if its as 'onstant K is 0.462 /Pa m K is 0.462 /Pa m33J / L.J / L. Ans.
Ans. 2.)! 2.)! /Jm/Jm33 2).
2). At At 3232oo5 and 20) /Pa5 and 20) /Pa ae, the spe'i' ae, the spe'i' weiht of a 'ertain as weiht of a 'ertain as was 13.* IJm
was 13.* IJm33.. 7etermine the as 7etermine the as 'onstant of this as. 'onstant of this as. Ans.
Ans. *18.8* *18.8* J/ J/ L L FLUID MECHANICS and FLUID MECHANICS and HYDRAULICS
HYDRAULICS SET 2
SET 2 26.
26. #hat #hat is is the the spe'i'spe'i' weiht if air at a weiht if air at a temperat"re of 30 temperat"re of 30oo55 and a press"re of 4*0 and a press"re of 4*0 /Pa abs. /Pa abs. Ans.
Ans. 0.0)2! 0.0)2! /IJm/IJm33 2*.
2*. Air Air is is /ept /ept at at aa press"re of 200 /Pa abs press"re of 200 /Pa abs and a temperat"re of and a temperat"re of 30
30oo5 in a )00 liter5 in a )00 liter 'ontainer. #hat is the 'ontainer. #hat is the mass of air
mass of air Ans.
Ans. 1.1) 1.1) // 28.A as at 40
28.A as at 40oo5 "nder a5 "nder a press"r
press"re of e of 21.868 bar21.868 bar
abs has a "nit weiht of abs has a "nit weiht of 362 IJm
362 IJm33. #hat is the. #hat is the &al"e of K for this as &al"e of K for this as Ans.
Ans. 1!.3 1!.3 mJL mJL ABSOLUTE AND ABSOLUTE AND
KINEMA
KINEMATIC TIC VISCOSITY VISCOSITY 2!. -f the &is'osity of water 2!. -f the &is'osity of water
at 68
at 68ooF is 0.01008 poise,F is 0.01008 poise, 'omp"te its absol"te 'omp"te its absol"te &is'osity in
&is'osity in po"ndse'ondpo"ndse'ond per s$"are foot. -f the per s$"are foot. -f the spe'i' ra&ity at 68 spe'i' ra&ity at 68ooF isF is 0.!!8, 'omp"te its 0.!!8, 'omp"te its /inemati' &is'osity in /inemati' &is'osity in s$"are feet per se'ond. s$"are feet per se'ond. Iote? 1 lb.sJft
Iote? 1 lb.sJft22 E 4*8.8 E 4*8.8 poises. poises. Ans. 2.1110 Ans. 2.1110)) lb.sJft lb.sJft22,, 1.0!10 1.0!10))ftft22Js.Js.
30.-f the &is'osity of water at 30.-f the &is'osity of water at
*0
*0oo5 is 0.00402 poise and5 is 0.00402 poise and its spe'i' ra&ity is its spe'i' ra&ity is 0.!*8, determine its 0.!*8, determine its absol"te &is'osity in absol"te &is'osity in PasPas and its /inemati'
and its /inemati' &is'osity in m
&is'osity in m22Js and inJs and in sto/es.
sto/es. Ans.
Ans. 0.000402 0.000402 Pas,Pas, 4.1110 4.1110** m m22Js, 4.1110Js, 4.111033 sto/e sto/e 31.5on&ert 1).14 poises to 31.5on&ert 1).14 poises to /inemati' &is'osity in ft /inemati' &is'osity in ft22JsJs if the li$"id has a spe'i' if the li$"id has a spe'i' ra&ity of 0.!64.
ra&ity of 0.!64. Ans.
Ans. 0.016! 0.016! ftft22JsJs
32.
32. <<wo lare wo lare planeplane s"rfa'es are 2) mm s"rfa'es are 2) mm apart and the spa'e apart and the spa'e between them is lled between them is lled with a li$"id of &is'osity with a li$"id of &is'osity of 0.!)8 Pas. Ass"min of 0.!)8 Pas. Ass"min the &elo'ity radient to the &elo'ity radient to be a straiht line, what be a straiht line, what for'e is re$"ired to p"ll a for'e is re$"ired to p"ll a &ery thin plate of 0.3* &ery thin plate of 0.3* m
m22 area at a 'onstant area at a 'onstant speed of 0.3 mJs if the speed of 0.3 mJs if the plate is 8.4 mm from plate is 8.4 mm from one of the s"rfa'es one of the s"rfa'es Ans. Ans. 1!.06 1!.06 II BULK MODULUS OF BULK MODULUS OF ELASTICITY ELASTICITY 33. A li$"id 'ompressed in a 33. A li$"id 'ompressed in a 'ylinder has a &ol"me of 'ylinder has a &ol"me of 1000 'm
1000 'm33 at 1 IJm at 1 IJm22 and a &ol"me of !!) 'm and a &ol"me of !!) 'm33 at 2 IJm
at 2 IJm22. #hat is its. #hat is its b"l/ mod"l"s of b"l/ mod"l"s of elasti'ity, L elasti'ity, L Ans.
Ans. 200 200 PaPa 34.
34. #hat #hat press"re ispress"re is re$"ired to red"'e the re$"ired to red"'e the &ol"me of water by &ol"me of water by 0.6% 9"l/ mod"l"s of 0.6% 9"l/ mod"l"s of elasti'ity of water, H E elasti'ity of water, H E 2.2 Pa. 2.2 Pa. Ans.
Ans. 13.2 13.2 PaPa 3). Find the b"l/ mod"l"s 3). Find the b"l/ mod"l"s of elasti'ity of a li$"id if of elasti'ity of a li$"id if a press"re of 1)0 psi a press"re of 1)0 psi applied to 10 ft applied to 10 ft33 of the of the
li$"id 'a"ses a &ol"me li$"id 'a"ses a &ol"me red"'tion of 0.02 ft red"'tion of 0.02 ft33.. Ans.
Ans. *)000 *)000 psipsi 36.
36. Find Find the 'hane inthe 'hane in &ol"me of 1 ft
&ol"me of 1 ft33 of water of water at 80
at 80ooF when s"b@e'tedF when s"b@e'ted to a press"re in'rease of to a press"re in'rease of 300 psi. #aterMs b"l/ 300 psi. #aterMs b"l/ mod"l"s of elasti'ity at mod"l"s of elasti'ity at this temperat"re is 32) this temperat"re is 32) 000 psi 000 psi Ans. Ans. 0.000!2 0.000!2 ftft33 3*. #ater in a hydra"li' 3*. #ater in a hydra"li'
press, initially at 13* /Pa press, initially at 13* /Pa abs, is s"b@e'ted to a abs, is s"b@e'ted to a press"r
press"re of e of 116,280 /Pa116,280 /Pa abs. Nsin H E 2.) Pa, abs. Nsin H E 2.) Pa, determine the
determine the
per'entae de'rease in per'entae de'rease in the &ol"me of water. the &ol"me of water. Ans.
Ans. 4.6)% 4.6)% de'reasede'rease COMPRESSION OF COMPRESSION OF
GASSES GASSES 38.
38. -f -f a a &essel &essel thatthat 'ontains 3,)00 ft 'ontains 3,)00 ft33 of of water at )0 water at )0ooF G62.4 p'fCF G62.4 p'fC atmospheri' press"re is atmospheri' press"re is heated to 160 heated to 160ooF G61 p'fC,F G61 p'fC, what will be the
what will be the
per'entae 'hane in its per'entae 'hane in its &ol"me #hat weiht of &ol"me #hat weiht of water m"st be remo&ed water m"st be remo&ed to maintain the oriinal to maintain the oriinal &ol"me
&ol"me Ans.
Ans. 2.*% 2.*% in'rease,in'rease, 4.!0 lb
3!. A &erti'al, 'ylindri'al 3!. A &erti'al, 'ylindri'al
tan/ with a diameter of tan/ with a diameter of 12.00 m and a depth of 12.00 m and a depth of 4.00 m is lled to the 4.00 m is lled to the top with water at 20 top with water at 20oo55 G!.*! /IJm
G!.*! /IJm33C. -f theC. -f the water is heated )0 water is heated )0oo55 G!.6! /IJm
G!.6! /IJm33C, howC, how m"'h water will spill m"'h water will spill o"t
o"t Ans.
Ans. 4.* 4.* mm33 40.
40. -f -f ! ! mm33 of an ideal of an ideal as at 24
as at 24oo5 and 1)05 and 1)0 /Paa is 'ompressed to /Paa is 'ompressed to 2 m
2 m33, GaC what is the, GaC what is the res"ltin press"re res"ltin press"re ass"min isothermal ass"min isothermal 'onditions, GbC what 'onditions, GbC what wo"ld ha&e been the wo"ld ha&e been the press"re and
press"re and temperat"re if the temperat"re if the pro'ess is
pro'ess is isentropi'isentropi'.. Nse / E 1.3.
Nse / E 1.3. Ans.
Ans. 6*) 6*) /Paa, /Paa, 10601060 /Paa, 466.4 L or /Paa, 466.4 L or 1!3.4
1!3.4oo55
41.eli"m at 14! /Pa abs 41.eli"m at 14! /Pa abs
and 10 and 10oo5 is5 is isentropi'ally isentropi'ally 'ompressed to one 'ompressed to one forth of its oriinal forth of its oriinal &ol"me. #hat is its nal &ol"me. #hat is its nal &ol"me / E 1.66 &ol"me / E 1.66 Ans.
Ans. 1488 1488 /Pa /Pa absabs 42.
42. -f 12 -f 12 mm33of nitroen atof nitroen at 30
30oo5 and 12) /Pa abs is5 and 12) /Pa abs is
permitted to epand permitted to epand isothermally to 30 m isothermally to 30 m33,, what is the res"ltin what is the res"ltin press"r
press"re e #hat wo"ld#hat wo"ld ha&e been if the
ha&e been if the pro'esspro'ess had been isentropi' / E had been isentropi' / E 1.40
1.40 Ans.
Ans. )0 )0 /Paa, /Paa, 34.*34.* /Paa
/Paa SURF
SURFACE TENSION ACE TENSION ANDAND CAPILLARITY
CAPILLARITY
43. #hat is the &al"e of the 43. #hat is the &al"e of the s"rfa'e tension of a small s"rfa'e tension of a small drop of water 0.) mm in drop of water 0.) mm in diameter whi'h is in diameter whi'h is in 'onta't with air if the 'onta't with air if the press"re within the press"re within the droplet is )61 Pa droplet is )61 Pa Ans.
Ans. 0.042 0.042 IJmIJm FLUID MECHANICS and FLUID MECHANICS and HYDRAULICS
HYDRAULICS SET 3
SET 3 44.
44. A A small small drop drop of of waterwater at 80
at 80ooF is in 'onta't withF is in 'onta't with the air and has a
the air and has a
diameter of 0.02 in. -f the diameter of 0.02 in. -f the press"re within the press"re within the droplet is 0.082 psi droplet is 0.082 psi reater than the reater than the atmospher
atmosphere, what e, what is theis the &al"e of the s"rfa'e &al"e of the s"rfa'e tension tension Ans. Ans. 0.004!2 0.004!2 lbJftlbJft 4). An atomier forms 4). An atomier forms water droplets 4) water droplets 4)
µµ
m inm in diameter. 7etermine the diameter. 7etermine the e'ess press"re within e'ess press"re within these droplets "sin these droplets "sinσ
σ
E E 0.0*12 IJm.0.0*12 IJm. Ans.
Ans. 632! 632! PaPa
46.<wo 'lean, parallel lass 46.<wo 'lean, parallel lass plates, separated by a plates, separated by a distan'e d E 1.) mm, distan'e d E 1.) mm, are dipped in a bath of are dipped in a bath of water. ow far does the water. ow far does the water rise d"e to water rise d"e to 'apillary a'tion, if 'apillary a'tion, if s"rfa'e tension s"rfa'e tension
σ
σ
E E 0.0*30 IJm 0.0*30 IJm Ans.Ans. !.!4 !.!4 mmmm 4*.
4*. Hstimate tHstimate the heiht he heiht toto whi'h water will rise in a whi'h water will rise in a 'apillary t"be of
'apillary t"be of diameter 3 mm. Nse diameter 3 mm. Nse
σ
σ
E E 0.0*28 IJm.0.0*28 IJm. Ans.
Ans. !.! !.! mmmm 48.
48. A lass A lass of of t"be t"be isis inserted in mer'"ry, the inserted in mer'"ry, the 'ommon temperat"re is 'ommon temperat"re is 20
20oo5. #hat is the5. #hat is the "pward for'e on the "pward for'e on the lass as a res"lt of lass as a res"lt of s"rfa'e e(e'ts "rfa'e s"rfa'e e(e'ts "rfa'e tension E 0.)14 IJm, d tension E 0.)14 IJm, dii E 2) mm and d
E 2) mm and doo E 3) E 3) mm.
mm. Ans.
Ans. 0.0623 0.0623 II 4!.Hstimate the 'apillary 4!.Hstimate the 'apillary depression for mer'"ry depression for mer'"ry
in a lass t"be 2 mm in a lass t"be 2 mm diameter. Nse
diameter. Nse
σ
σ
E 0.)14 E 0.)14 IJm andIJm and
θθ
E 140 E 140oo.. Ans.Ans. ).! ).! mmmm depression depression )0.
)0. Hstimate Hstimate thethe
depression h for mer'"ry depression h for mer'"ry in the lass 'apillary in the lass 'apillary t"be. Anle
t"be. Anle
θθ
E 40 E 40oo, "nit, "nit weiht of water is !*!0 weiht of water is !*!0 IJm IJm33.. Ans. Ans. ).!1 ).!1 mmmm )1.)1. Find Find the 'apillary the 'apillary rise inrise in the t"be for a
the t"be for a mer'"rymer'"ry airla
airlass interfa'e ss interfa'e withwith
θθ
E 130
E 130oo if the t"be radi"s if the t"be radi"s is 1 mm and the is 1 mm and the temperat"re is 20 temperat"re is 20oo5.5. "rfa'e tension is 0.)14 "rfa'e tension is 0.)14 IJm. IJm. Ans. Ans. =).0 =).0 mmmm )2.
)2. Find Find the the 'apillary 'apillary riserise in the t"be for a water in the t"be for a water airlass interfa'e airlass interfa'e
θθ
E 0 E 0oo if the t"be is 1 mm if the t"be is 1 mm andand the temperat"re is 20 the temperat"re is 20oo5.5. "rfa'e tension is "rfa'e tension is 0.0*28 IJm. 0.0*28 IJm. Ans. Ans. 14.8 14.8 mmmm )3. )3. -f -f a a b"bble b"bble isis e$"i&alent to an air e$"i&alent to an air water interfa'e with water interfa'e with s"rfa'e tension 0.00) s"rfa'e tension 0.00) lbJft, what is the lbJft, what is the press"re di(eren'e press"re di(eren'ebetween the inside and o"tside of a b"bble of diameter 0.003 in Ans. 80.0 lbJft2 )4.At 30o5, what diameter
lass t"be is ne'essary to /eep the 'apillary heiht 'hane of water less than 2 mm "rfa'e tension is 0.0*12 IJm. Ans. 14.6 mm )).#hat for'e is re$"ired
to lift a thin wire rin 6 'm in diameter from a water s"rfa'e at 20o5 "rfa'e tension is 0.0*28 IJm. Ans. 0.02*4 I )6.#hat is the press"re
di(eren'e between the inside and o"tside of a 'ylindri'al water @et when the diameter is 2.2 mm and the temperat"re is 10o5 "rfa'e tension is 0.0*42 IJm. Ans. 6*.) Pa
)*.7istilled water stands in a lass t"be of ! mm diameter at a heiht of 24 mm. #hat is the tr"e stati' heiht Nse
σ
E 0.0*42 IJm. Ans. 20.64 mm)8.Find the anle the s"rfa'e tension lm lea&es the lass for a &erti'al t"be immersed in water if the diameter is 0.2) in and the 'apillary rise is 0.08 in. Nse
σ
E 0.00) lbJft )!.7istilled water at 10o5stands in a lass t"be of !.0 mm diameter at a heiht of 24.0 mm. #hat is the tr"e stati' heiht Nse
σ
E 0.0*42 IJm. FLUID STATICS60.A depth of li$"id of 1 m 'a"ses a press"re of * /Pa, what is the spe'i' ra&ity of li$"id Ans. 0.*14
61.#hat is the press"re 12.) m below the o'ean Nse sp. r. E 1.03 for salt water.
Ans. 126.3 /Pa 62. -f the press"re 23 m
below a li$"id is 338.44) /Pa, determine its "nit weiht, mass density, and spe'i' ra&ity. Ans. 14.*1) /IJm3, 1)00 /Jm3, 1.)
63.-f the press"re at a point in the o'ean is 60 /Pa, what is the press"re 2* m below this point
Ans. 332.82 /Pa 64.-f the press"re in the air
spa'e abo&e an oil Gs E 0.*)C s"rrfa'e in a 'losed tan/ is 11) /Pa absol"te, what is the press"re 2 m below the s"rfa'e
Ans. 28.41) /Pa 6).Find the absol"te
press"re in /Pa at a depth of 10 m below the free s"rfa'e of oil of sp. r. E 0.*) of the barometri' readin is *)2 mm.
Ans. 1*3.! /Pa FLUID MECHANICS and HYDRAULICS
SET 4 66.A press"re ae 6 m
abo&e the bottom of the tan/ 'ontainin a li$"id reads !0 /Pa.; another ae heiht 4 m reads 103 /Pa. 7etermine the spe'i' weiht of the li$"id.
Ans. 6.) /IJm3 6*.An open tan/ 'ontains
).8 m water 'o&ered with 3.2 m of /erosene G
γ
E 8 /IJm3C. Find the
press"re at the interfa'e and the bottom of the tan/.
Ans. 2).6 /Pa, 82.4!8 /Pa
68.-f atmospheri' press"re is !).* /Pa and the ae atta'hed to the tan/ reads 188 mm &a'""m, nd the absol"te press"re within the tan/.
Ans. *0.62 /Pa 6!. A weather report
indi'ates the barometri' press"re is 2!.*) in of mer'"ry. #hat is the atmospheri' press"re in psi
Ans. 14.61 psi *0.A press"re ae *.0 m
abo&e the bottom of a tan/ 'ontainin a li$"id reads 64.!4 /Pa, another ae at heiht 4.0 m reads 8*.)3 /Pa. 5omp"te the spe'i' weiht and mass density of the B"id.
Ans. *)60 IJm3, *86 /Jm3
*1.An open tan/ 'ontains ).* m of water 'o&ered with 2.8 m of /erosene G
γ
E 8.0 /IJm3C. Find the press"re at the interfa'e
and at the bottom of the tan/. Nnit weiht of water E !.*! /IJm3. Ans. 22.4 /Pa, *8.2 /Pa
*2.-f air had a 'onstant spe'i' weiht of 0.0*6 lbJft3 and were
in'ompressible, what wo"ld be the heiht of the atmosphere if sea le&el press"re were 14.!2 psia
Ans. 282*0 ft *3.<he weiht density of a
m"d is i&en by
γ
E 10 O 0.)h, whereγ
is in /IJm3 and h in m. 7etermine the press"re, in /Pa, at a depth of ) m. Ans. )6.2) /Pa *4.-f the absol"te press"rein a as is 40 psia and the atmospheri' press"re is 846 mbar abs, nd the ae press"re in psi, /Pa and bar.
Ans. 2*.* psi, 1!1 /Pa, 1.!13 bar *).-f the atmospheri'
press"re is 0.!0 bar abs and a ae atta'hed to a tan/ reads 3!0 mm &a'""m, what is
the absol"te press"re within the tan/ Nnit weiht of water is !.*! /IJm3.
Ans. 38.1 /Pa *6.-f air had a 'onstant
spe'i' weiht of 12.2 IJm3 and were
in'ompressible, what wo"ld be the heiht of the atmospheri' press"re Gsea le&elC is 102 /Pa Ans. 8360.66 m **.Ass"min spe'i' weiht
of air to be 'onstant at 12 IJm3, what is the
approimate heiht of t. 9anahaw if a mer'"ry barometer at the base of the mo"ntain reads 6)4 mm and at the same time another barometer at the top of the mo"ntain reads 480 mm. Ans. 1!34.)3 m *8.5on&ert *60 mm of mer'"ry to aC oil of sp. r. 0.82 and bC water. Ans. 12.60) m, 10.34 m
*!.A barometer reads *60 mm and a press"re ae atta'hed to a tan/ reads 8)0 'm of oil Gsp. r. E 0.80C. #hat is the
absol"te press"re in the tan/ in /Pa
Ans. 168.1 /Pa 80.Hpress an absol"te
press"re of ) atm in meters of water ae when the barometer reads *60 mm. Nnit weiht of water is !.*! /IJm3.
Ans. 41.4 m of water 81.Ass"min sea water to
ha&e a 'onstant spe'i' weiht of 10.0) /IJm3, what is the absol"te press"re at a depth of 10 /m
Ans. !!3 atm
82.A hydra"li' press is "sed to raise an 80/I 'aro tr"'/. -f oil of sp. r. 0.82 a'ts on the piston "nder a press"re of 10 Pa, what diameter of piston is re$"ired
GEOTECHNICAL ENGINEERING SET 1
SOIL COMPOSITION 1. <he moist "nit weiht of
a soil is 1!.2 /IJm3. i&en that s E 2.6! and water 'ontent is !.8 %. 7etermine? aC dry "nit
weiht, bC &oid ratio, 'C porosity, dC deree of sat"ration.
Ans. aC 1*.4!; bC 0.)08; 'C 0.33*; dC )1.*! % 2. For a i&en soil, the
followin are /nown. s E 2.*4, moist "nit weiht E 20.6 /IJm3, and moist"re 'ontent is 16.6 %. 7etermine the followin? aC dry "nit weiht, bC &oid ratio, 'C porosity, dC deree of sat"ration, eC weiht of water in /I to be added per '"bi' meter of soil for a 100 % deree of sat"ration.
Ans. aC 1*.6* ; bC 0.)2 ; 'C 0.34; dC 8*. ) %; eC 0.44
3. <he "nit weiht of soil is 1). 10 /IJm3. <he moist"re 'ontent of this soil is 1* % when the deree of sat"ration is 60 %. 7etermine the followin? aC &oid ratio, bC sp. r. of soil, 'C sat"rated "nit weiht. Ans. aC 0.)!; bC 2.10; 'C 16.)8
4. <he moist weiht of 0.00)* m3 of a soil is 102.6 I. <he moist"re
'ontent and the spe'i' ra&ity of soil solids are determined in the laboratory to be 11 % and 2.* respe'ti&ely. 5al'"late the followin? aC moist "nit weiht, bC dry "nit weiht, 'C &oid ratio, dC porosity, eC deree of sat"ration. Ans. aC 18; bC 16.22;
'C 0.63 ; dC 0.3! ; eC 46.!2 %
). -n its nat"ral state, a moist soil has a &ol"me of 0.00!3) m3 and weihs 1*8 I. <he o&en dried weiht of the soil is 1)4 I. -f s E 2.67, d!"#$n !% &'((')$n*+ a #'$-!"'ontent, bC moist "nit weiht, 'C dry "nit weiht, dC &oid ratio, eC porosity, fC deree of sat"ration. Ans. aC 1).6 % ; bC 1!.04 ; 'C 16.4* ; dC 0.)! ; eC 0.3* ; fC *0.6 %
6. <he dry density of sand with a porosity of 0.38* is 1600 /Jm3 ratio. 7etermine the
followin? aC &oid ratio, bC sp. r. of soil, 'C
sat"rated "nit weiht of soil in /IJm3.
Ans. aC 0.631; bC 2.61; 'C 1!.4!
*. <he moist "nit weiht of a soil is 16.) /IJm3. -f the water 'ontent is 1) % and sp. r. of soil is 2.*, determine the followin? aC dry "nit weiht, bC porosity, 'C deree of sat"ration; dC mass of water in /Jm3 to be added to rea'h f"ll sat"ration. Ans. aC 14.3); bC 0.4)8; 'C 4*.! %; dC 238.)
8. For a i&en sandy soil, ema E 0.*),emin E 0.46 and s E 2.68. -f the relati&e density of the soil 7r E *8 % and its water 'ontent is ! %, determine the followin? aC in sit" &oid ratio, bC moist "nit weiht of 'ompa'tion in /IJm3, 'C dry "nit weiht in /IJm3.
Ans. aC 0.)24; bC 18.8; 'C 1*.2)
!. Followin are the res"lts of a shrin/ae limit test? -nitial &ol"me of soil in a sat"rated state E 24.6 'm3
Final &ol"me of soil in a dry state E 1).! 'm3 -nitial mass in a sat"rated state E 44 Final mass in a dry state
E 30.1
7etermine the followin? aC shrin/ae limit of soil, bC &oid ratio if s E 2.*0, 'C dry "nit weiht Ans. aC 1*.28 %; bC 0.46*; 'C 18.06
10.<he moist "nit weiht of 0.00283 m3 of soil is )4.4 I. -f the moist"re 'ontent is 12 % and the spe'i' ra&ity of soil solids is 2.*2, determine the followin? aC moist "nit weiht, bC dry "nit weiht, 'C &oid ratio, dC porosity, eC deree of sat"ration, fC &ol"me o''"pied by water. Ans. aC 1!.22; bC 1*.16; 'C 0.)); dC 0.3); eC )!.3 %; fC 0.000)! m3 11.For a moist soil, the
followin are i&en? ol. 1.2 m3, weiht E 23.4 /I, water 'ontent E 8.6 % and s E 2.*1. 7etermine the followin? aC "nit weiht, bC dry "nit weiht, 'C &oid ratio,
dC porosity, eC deree of sat"ration, fC &ol. o''"pied by water. Ans. aC 1!.2 ; bC 1*.68 ; 'C 0.)04 ; dC 0.33) ; eC 46.2 % ; fC 0.186 GEOTECHNICAL ENGINEERING SET 2
12.For a sat"rated soil, the followin are i&en? water 'ontent E 23 %, s E 2.6*. 7etermine the followin? aC sat"rated "nit weiht, bC dry "nit weiht, 'C moist "nit weiht when the deree of sat"ration be'omes *0 %.
Ans. aC 1!.!6; bC 16.23; 'C 18.84 /IJm3
13.<he dry density of a soil is 1*)0 /Jm3. pe'i' ra&ity of soil is 2.66. 7etermine the followin? aC moist"re 'ontent when it is sat"rated bC sat"rated "nit weiht, 'C e(e'ti&e "nit weiht of soil in /IJm3. Ans. aC 1!.)) % ; bC 20.)2 ; 'C 10.*1 14.<he porosity of a soil is
7etermine the followin? aC sat. "nit weiht, bC moist"re 'ontent when the moist "nit weiht is 1*.), 'C shrin/ae limit.
Ans. aC 20.)8; bC 2.1 %; 'C 20.0* %
1).<he moist "nit weiht and derees of sat"rated of a soil are i&en in the followin table.
γ
GLIJm3C G %C 16.64 /IJm3 )0 1*.*3 /IJm3 *) 7etermine thefollowin? aC &oid ratio, bC sp. r. of soil, 'C sat"rated "nit wt., dC weiht of water in /I that is in 0.128 m3 of the soil when it is sat"rated.
Ans. aC 0.*8; bC 2.6); 'C 18.82; dC 2.40
16.For sandy soil, ema E 0.86,emin E 0.43 and s E 2.66.
aC #hat is the &oid ratio at 7r E )6 %. Ans. 0.62
bC #hat is the moist "nit weiht of soil when water 'ontent is * %. Ans. 1*.24 /IJm3 'C #hat is the deree of
sat"ration Ans. 30 % 1*.A soil sample has the
followin properties? Porosity E 0.38! pe'i' ra&ity E 2.*) aC 5omp"te the &oid ratio of the soil sample. Ans. 0.66
bC 5omp"te the sat"rated "nit weiht of soil sample.
Ans. 20.1)
'C 5omp"te the e(e'ti&e "nit weiht of the soil sample.
Ans. 18.34
18.A soil sample ta/en from the ro"nd has a
moist"re 'ontent of 12 % and deree of sat"ration of )2 %. -f its spe'i' ra&ity is 2.*. 7etermine the followin? aC &oid ratio, bC sat"rated "nit weiht, 'C "nit weiht. Ans. aC 0.62; bC 20.10;
'C 10.2!
1!.A soil sample has a dry "nit weiht of 1*.1 /IJm3 and a &oid ratio of 0.)2.
7etermine the followin? aC sp. r. of soil, bC "nit weiht of soil, 'C shrin/ae limit.
Ans. aC 2.6); bC 10.6); 'C 1*.62 %
20.<he &ol"me of the soil sample meas"red before dryin is 110 'm3. <he wet "nit weiht of soil is 20* and the dried wet of the soil sample is 163 . -f the sp. r. of the soil is 2.68, determine the followin? aC &oid ratio, bC deree of sat"ration, 'C shrin/ae limit. Ans. aC 0.81; bC 8!.3 %; 'C 30.22 %
21.A sample of silty sand has the followin properties ? p. r. E 2.6*
hrin/ae limit E 23.22 %
aC 5omp"te the porosity of the silty sand.
Ans. 0.383
bC 5omp"te the relati&e density of the sand if it has a &oid ratio in the loosest 'ondition of 0.!0 and a &oid ratio of 0.30 in the densest 'ondition. Ans. 46.6* %
'C 5omp"te the e(e'ti&e "nit weiht of the silty sand.
Ans. 10.11 /IJm3 22.A sat"rated soil sample
has the followin data? #ater 'ontent E 34 % oids ratio E 0.!2 7etermine the followin? aC sp. r. of soil, bC e(e'ti&e "nit weiht, 'C moist "nit weiht. Ans. aC 2.*1; bC 8.*4; 'C 18.))
23.<he net weiht of a soil spe'imen before dryin is 20* and its dried weiht after dryin in an o&en is 163 . <he &ol"me of the spe'imen before dryin is 120 'm3. p. r. of soil sample is 2.62.
aC 5omp"te the moist"re 'ontent of the water.
Ans. 2* % bC 5omp"te the &oid ratio.
Ans. 0.!3
'C 5omp"te the deree of sat"ration.
Ans. *6.1 % GEOTECHNICAL ENGINEERING
SET 3
24.<he porosity of the soil is 0.3) and its moist "nit weiht is 1*.) /IJm3. <he sp. r. of the soil is 2.6!.
aC #hat is the moist"re 'ontent of the soil Ans. 2.13 % bC 5omp"te the deree of sat"ration.
Ans. 10.61 % 'C 5omp"te the shrin/ae limit of soil. Ans. 20.0* % 2).<he e(e'ti&e "nit
weiht of soil is 10.2! /IJm3. oid ratio of the soil is 0.62.
aC 5omp"te the sp. r. of the soil.
Ans. 2.*0
bC -f the water 'ontent of the soil is 14 %, 'omp"te for the deree of sat"ration.
Ans. 60.!* % 'C 5omp"te the shrin/ae limit. Ans. 22.!6 % 26.A silty 'lay has a plasti'
limit of 2) and a plasti'ity inde of 30. -f the 'lay has a li$"idity inde of 0.20.
aC 5omp"te the water 'ontent of the 'lay. Ans. 31 %
bC 5omp"te the deree of sat"ration if the sp. r. of the 'lay is 2.*0 and a &oid ratio of 0.!2 Ans. !0.!8 % 'C 5omp"te the moist "nit weiht of the 'lay if the &oid ratio is 0.!2, s E 2.*0
Ans. 18.0* /IJm3 2*.<he shrin/ae limit of a
soil sample is 14.3 %. -f the &oid ratio is e$"al to 0.38 and water 'ontent is 12.6 %. 7etermine the followin? aC sp. r. of soil, bC deree of sat"ration of the soil, 'C moist "nit weiht of the soil.
Ans. aC 2.66; bC 88.2 %; 'C 21.21 /IJm3
28.A ran"lar soil was tested in the laboratory and fo"nd to ha&e a ma. and min. &oid ratios of 0.84 and 0.38 respe'ti&ely. -f the relati&e density of the soil is 6!.6 %, sp. r. of soil is 2.*0.
aC 5omp"te the in sit" &oid ratio of the soil. Ans. 0.)2
bC 5omp"te the shrin/ae limit of soil. Ans. 1!.26 % 'C 5omp"te the
e(e'ti&e "nit weiht of soil.
Ans. 10.** /IJm3 2!.A soil has a moist"re
'ontent of 18.2 % and a deree of sat"ration of 80 %. -f the &oid ratio of soil is 0.60*. 7etermine the followin? aC sp. r. of the soil, bC moist "nit weiht of the soil, 'C sat"rated "nit weiht of soil.
Ans. aC 2.6*; bC 1!.2* /IJm3; 'C 20 /IJm3 30.For a i&en sandy soil
with ma. and min. &oid ratios of 0.*) and 0.46 respe'ti&ely has a sp. r. of 2.68. -f the density inde is *8 % and moist"re 'ontent of ! %. aC #hat wo"ld be the in sit" &oid ratio
Ans. 0.)238 bC 7etermine the deree of sat"ration of the soil.
Ans. 46.0) % 'C #hat will be the moist "nit wt. of
'ompa'tion in the eld
Ans. 18.81 /IJm3 31.A sample of soft
sat"rated 'lay has a &ol"me of 100 '". m. and weihs 1*) . -f the o&en dry weiht is 120 .
aC 5omp"te the water 'ontent of 'lay. Ans. 4).8 % bC 5omp"te the &oid ratio of the 'lay. Ans. 1.22
'C 5omp"te the sp. r. of the 'lay.
Ans. 2.66
32.<he shrin/ae limit of a soil sample is 16.) % and the sp. r. of the soil sample is 2.6). A sample of this soil weihs 4).36 when wet and 40.) when dry.
aC 5omp"te the &oid ratio of the soil sample. Ans. 0.44
bC 5omp"te the deree of sat"ration of the soil. Ans. *2 %
'C 5omp"te the wet "nit weiht of the water. Ans. 20.22 /IJm3 33.A shrin/ae limit of a
soil sample is e$"al to 24.81 %. -t is fo"nd to ha&e a moist"re 'ontent
of 18 % and a sp. r. of 2.*0. 7etermine the followin? aC &oid ratio, bC deree of sat"ration, 'C air &oid ratio. Ans. aC 0.6*; bC *2.)4 %; 'C 0.11 GEOTECHNICAL ENGINEERING SET 4
34.<he air ratio of a soil sample is e$"al to 0.12 and a porosity of 0.40. -f the sp. r. of the soil sample is 2.*0. 7etermine the
followin? aC deree of sat"ration, bC water 'ontent, 'C shrin/ae limit.
Ans. aC *0 %; bC 1*.3* %; 'C 24.81 %
3).A sample of "niform sand has a porosity of 43 %. From the lab test, the radi"s of the &oid ratio in the loosest 'ondition is 0.8) and the &oid ratio of 0.3) in the densest 'ondition. -f the water 'ontent is 12 %. s E 2.68. 7etermine the
followin? aC density inde, bC deree of sat"ration, 'C air &oid ratio.
Ans. aC 20 %; bC 42.!* %; 'C 0.24)
36.<he 'riti'al hydra"li' radient for a soil sample is e$"al to 1.02. if the spe'i' ra&ity of the soil sample is 2.6* and the water 'ontent is 14 %. aC 5omp"te the &oid ratio of the soil sample. Ans. 0.64
bC 5omp"te the deree of sat"ration.
Ans. )8.40 % 'C 5omp"te the dry "nit weiht at ero air &oids. Ans. 1!.0* /IJm3 3*.<he dry "nit weiht of soil
at ero air &oids is e$"al to 1! /IJm3. <he soil has a water 'ontent of 12 % and a deree of
sat"ration of )8 %. 5omp"te the followin? aC spe'i' ra&ity, bC &oid ratio, 'C air &oid ratio. Ans. aC 2.)2; bC 0.)2 ; 'C 0.144
38.-n its nat"ral state a moist soil has a &ol"me of 0.00! m3 and weihs 180 I. <he o&en dry weiht of
the soil is 1)0 I. -f the soil has a sp. r. of 2.*0, 'omp"te the followin? aC moist"re 'ontent, bC &oid ratio, 'C deree of sat"ration. Ans. aC 20 %; bC 0.)!; 'C !1.)3 %
3!.<he moist "nit weiht of soil is 1* /IJm3 with a moist"re 'ontent of 14 %. -f its sp. r. E 2.*, 'omp"te the followin? aC &oid ratio, bC porosity, 'C deree of sat"ration.
Ans. aC 0.*8; bC 0.438; 'C 48.46 %
40.<he 'lay density of the soil is 1800 /Jm3 with a sp. r. of 2.*. 5omp"te for the followin? aC &oid ratio, bC porosity, 'C moist"re 'ontent of the soil when f"lly
sat"rated.
Ans. aC 0.)0; bC 0.333; 'C 18.)2 %
41.<he weiht of the soil before dryin is 200 and its dried weiht after dryin is 160 . p. r. of soil E 2.6. ol. of soil before dryin is 120 'm3. 5omp"te the followin? aC water
'ontent, bC &oid ratio, 'C deree of sat"ration. Ans. aC 2) %; bC 0.!); 'C 68.4 %
42.A soil sample has a weiht of 120 before it was pla'ed on the o&en. After dryin for 20 min. it weihs only 100 . pe'i' ra&ity of soil sample is 2.6. ol"me of soil spe'imen before dryin is 66 'm3. 5omp"te for the followin? aC water 'ontent, bC &oid ratio, 'C deree of sat"ration. Ans. aC 20 %; bC 0.*2; 'C *2.* %
43.ilty sand has a &oid ratio in loosest 'ondition e$"al to 0.86 and a &oid ratio of 0.30 in the densest 'ondition. -f the relati&e density of sand is )4 %, 'omp"te the followin? aC in sit" &oid ratio, bC porosity, 'C if the dry "nit wt. of the silty sand is 16.8) /IJm3, 'omp"te the spe'i' ra&ity of sand. Ans. aC 0.)6; bC 0.36; 'C 2.68
44.<he 'lay "nit weiht of silty sand is 16.43