PREPARED BY EMS-CETSC

PREPARED BY EMS-CETSC

PRESENTED BY JOHN ERIC FERRANCO

### Introductory Concepts,

### Introductory Concepts,

### Definition and Units

### Definition and Units

1.) 100g of water is mixed to 150g of alcohol 1.) 100g of water is mixed to 150g of alcohol

(ρ=

(ρ=790kg/m790kg/m33_{). Calculate a) the specific}_{). Calculate a) the specific}

gravity (RD) of the mixture; b) the specific gravity (RD) of the mixture; b) the specific volume of the solution.

2.) A 45cm cube of ice melts, the liquid water 2.) A 45cm cube of ice melts, the liquid water is placed in a spherical container filling it. If is placed in a spherical container filling it. If the specific volume of ice at 0

the specific volume of ice at 0⁰C⁰C isis 1.094cm

1.094cm33_{/g and of water is 1.002cm}_{/g and of water is 1.002cm}33_{/g,}_{/g,}

determine the diameter of the spherical determine the diameter of the spherical vessel used.

3.) A two compartment vessel contains a fluid 3.) A two compartment vessel contains a fluid in each section. For the first compartment the in each section. For the first compartment the fluid density is 1200kg/m

fluid density is 1200kg/m33 _{and of the second}_{and of the second}

is 500kg/m

is 500kg/m33_{. The partition is removed and}_{. The partition is removed and}

the fluid mix. Determine the density of the the fluid mix. Determine the density of the mixture if

mixture if

a) the fluid masses are equal; a) the fluid masses are equal; b) the fluid

4.) A student on vacation went to scale Mt. 4.) A student on vacation went to scale Mt. Apo. His weight at the base of the mountain, Apo. His weight at the base of the mountain, where g=9.8m/s

where g=9.8m/s22 _{is 540N, on the top he}_{is 540N, on the top he}

weight 539.5N. Note that gravity acceleration weight 539.5N. Note that gravity acceleration decreases by 0.003m/s

decreases by 0.003m/s22 _{per 1000m ascent.}_{per 1000m ascent.}

Find the height in meters if Find the height in meters if a) Mt. Apo;

a) Mt. Apo;

b) a point above the base where the weight of b) a point above the base where the weight of an object decreases by 2%.

5.) A balloon is descending with a constant 5.) A balloon is descending with a constant acceleration of 3.5m/s

acceleration of 3.5m/s22_{. The mass of the}_{. The mass of the}

balloon with its basket and content is 80kg. balloon with its basket and content is 80kg. What mass of the ballast must be released so What mass of the ballast must be released so that the balloon will accelerate upward with a that the balloon will accelerate upward with a constant acceleration of 3.5m/s

constant acceleration of 3.5m/s22_{? Neglect air}_{? Neglect air}

resistance. resistance.

6.) A 40kN tank weighs 64kN when filled with 6.) A 40kN tank weighs 64kN when filled with kerosene and 70kN when filled with the same kerosene and 70kN when filled with the same volume of water. Find the specific gravity of volume of water. Find the specific gravity of kerosene.

7.) A solid cube material is 0.75cm on each 7.) A solid cube material is 0.75cm on each side. If it floats in oil of density 800kg/m side. If it floats in oil of density 800kg/m33

with 1/3 of the block out of oil, what is the with 1/3 of the block out of oil, what is the density of the material of the cube?

8.) The system shown is in equilibrium. 8.) The system shown is in equilibrium. Determine the diameter of the outside sphere Determine the diameter of the outside sphere if the submerged sphere has a diameter of if the submerged sphere has a diameter of 35cm.

9.) A block of wood with uniform horizontal 9.) A block of wood with uniform horizontal section floats in water with 20cm projecting section floats in water with 20cm projecting above the surface. The same block when above the surface. The same block when placed in a body of oil (SG=0.8) floats with placed in a body of oil (SG=0.8) floats with 18cm projecting above the oil surface. 18cm projecting above the oil surface. Determine the specific gravity of the wood.

10.) Determine the maximum weight W which 10.) Determine the maximum weight W which could be carried by the 45kg composite could be carried by the 45kg composite piston shown, if the pressure of gas A is piston shown, if the pressure of gas A is 350kPa, gas B and C have pressure of 170 350kPa, gas B and C have pressure of 170 and 500kPa,

11.) For the open manometer shown in the 11.) For the open manometer shown in the figure, what is the pressure in kPa at A figure, what is the pressure in kPa at A (a=30cm; b=48cm; RD

12.) For the differential manometer shown in 12.) For the differential manometer shown in the figure, determine the pressure difference the figure, determine the pressure difference between points X and Y when: Fluid X

between points X and Y when: Fluid X and Y isand Y is brine (RD=1.15), gage fluid is oil (RD=0.9) brine (RD=1.15), gage fluid is oil (RD=0.9) and z=90cm.

13.) CHALLENGE! 13.) CHALLENGE!

A cubical block of wood 0.1m on a side and A cubical block of wood 0.1m on a side and with a density of 550kg/m

with a density of 550kg/m33 _{floats in a jar of }_{floats in a jar of }

water. Oil with a density of 750kg/m

water. Oil with a density of 750kg/m33 _{is}_{is}

poured on the water until the top of the oil poured on the water until the top of the oil layer is 0.035m below the top of t

layer is 0.035m below the top of the block.he block. a) How deep is the oil layer?

a) How deep is the oil layer?

b) What is the gauge pressure at the

b) What is the gauge pressure at the block’sblock’s

lower face? lower face?

### Conservation of Mass and

### Conservation of Mass and

### Energy

### Energy

1.) Air flows through a compressor under 1.) Air flows through a compressor under steady flow condition. A suction: steady flow condition. A suction:

ν
ν_{1}_{1}=0.75m=0.75m33_{/kg,}_{/kg,} _{υ}_{υ}
1
1=30m/s. At discharge=30m/s. At discharge
ν
ν_{2}_{2}=0.25m=0.25m33_{/kg,}_{/kg,} _{υ}_{υ}
2

2=40m/s. determine the=40m/s. determine the

diameter ratio of the discharge pipe to that

diameter ratio of the discharge pipe to that of of the suction pipe.

2.) A 200g

2.) A 200g apple is thrown from the edge of aapple is thrown from the edge of a tall building with an initial speed of 20m/s. tall building with an initial speed of 20m/s. What is the change in kinetic energy of the What is the change in kinetic energy of the apple if it strikes the ground at 50m/s?

3.) What retarding force is required to stop a 3.) What retarding force is required to stop a 0.45 caliber bullet of mass 20g and a speed 0.45 caliber bullet of mass 20g and a speed of 300m/s as it penetrates a wooden block to of 300m/s as it penetrates a wooden block to a depth of 2 inches?

4.) A 40g rifle bullet is fired with a speed if 4.) A 40g rifle bullet is fired with a speed if 300m/s into a ballistic pendulum of mass 300m/s into a ballistic pendulum of mass 5kg suspended from a chord 1m long. 5kg suspended from a chord 1m long. Compute the vertical height through which Compute the vertical height through which the pendulum rises.

5.) A force F inclined at 30

5.) A force F inclined at 30⁰⁰ with thewith the horizontal moves an object horizontally a horizontal moves an object horizontally a distance of 8m. Determine the work done if distance of 8m. Determine the work done if F=7.5x+0.4x

F=7.5x+0.4x22_{, where F is in Newton and the}_{, where F is in Newton and the}

x is in meter. x is in meter.

6.) A wooden spherical ball with specific 6.) A wooden spherical ball with specific gravity of 0.42 and a diameter of 30cm is gravity of 0.42 and a diameter of 30cm is dropped from a height of 4.2m above the dropped from a height of 4.2m above the surface of the water in a pool. If the ball surface of the water in a pool. If the ball barely touches the bottom of the pool, what barely touches the bottom of the pool, what is the water level in the pool at

7.) A project engineer notices the site of a 7.) A project engineer notices the site of a former sawmill along a river. Ruins of the former sawmill along a river. Ruins of the original dam used as a hydropower source is original dam used as a hydropower source is still visible. The engineer decided to make still visible. The engineer decided to make some measurements to determine the some measurements to determine the maximum power that can be generated if the maximum power that can be generated if the site were rehabilitated; the stream flow is site were rehabilitated; the stream flow is found to be 25m

found to be 25m33_{/s and the change in}_{/s and the change in}

elevation is 4.87m. Determine the maximum elevation is 4.87m. Determine the maximum power that could be

8.) A 3kg block initially at rest us dropped 8.) A 3kg block initially at rest us dropped from a height of 0.5m onto a spring whose from a height of 0.5m onto a spring whose scale is 2940N/m. Find the maximum scale is 2940N/m. Find the maximum distance x that the spring will be distance x that the spring will be compressed. Assume g=9.8m/s

9.) A gas contained in a piston cylinder has
9.) A gas contained in a piston cylinder has
following initial properties: 3000kPa, 0.03m
following initial properties: 3000kPa, 0.03m33_{..}

The gas is compressed during the process The gas is compressed during the process where PV

where PV1.41.4_{=C to a pressure of 9000kPa. The}_{=C to a pressure of 9000kPa. The}

heat transfer from the gas is 3kJ. Determine heat transfer from the gas is 3kJ. Determine the change in internal energy, neglect the change in internal energy, neglect changes in kinetic and

10.) Steam enters the turbine with a pressure 10.) Steam enters the turbine with a pressure P=4800kPa, u=2950kJ/kg, h=3300kJ/kg, P=4800kPa, u=2950kJ/kg, h=3300kJ/kg, and with a flow of 6kg/s. Steam leaves with and with a flow of 6kg/s. Steam leaves with h=2300kJ/kg, u=2100kJ/kg and P=22kPa. h=2300kJ/kg, u=2100kJ/kg and P=22kPa. The radiative heat loss is equal to 24kJ/kg of The radiative heat loss is equal to 24kJ/kg of steam. Determine a) the power produced; b) steam. Determine a) the power produced; b) the adiabatic power; c) the inlet specific the adiabatic power; c) the inlet specific volume; d) the exit velocity if the exit area is volume; d) the exit velocity if the exit area is 0.5m

11.) Carbon Dioxide

11.) Carbon Dioxide (ρ=(ρ=1.8kg/m1.8kg/m33_{) having an}_{) having an}

enthalpy of 96.5kJ/kg enters a compressor. It enthalpy of 96.5kJ/kg enters a compressor. It leaves with an enthalpy of 175kJ/kg. There is leaves with an enthalpy of 175kJ/kg. There is 35kJ/kg of heat lost from the compressor as 35kJ/kg of heat lost from the compressor as CO

CO_{2}_{2} passes through it. Neglecting changes inpasses through it. Neglecting changes in
kinetic and potential energies, determine the
kinetic and potential energies, determine the
power required for a flow rate of 0.2225m

12.) CHALLENGE! A centrifugal compressor 12.) CHALLENGE! A centrifugal compressor

compresses 5.7m

compresses 5.7m33_{/min of air from 83kPaa to}_{/min of air from 83kPaa to}

620kPaa. The initial density is 1.27kg/m

620kPaa. The initial density is 1.27kg/m33 _{and}_{and}

the final density is 4.8kg/m

the final density is 4.8kg/m33_{. The inlet}_{. The inlet}

suction line is 10cm in

suction line is 10cm in diameter and thediameter and the

discharge line is 5cm in diameter. Determine discharge line is 5cm in diameter. Determine a) the mass flow rate; b) the change in flow a) the mass flow rate; b) the change in flow energy between boundaries; c) the kinetic energy between boundaries; c) the kinetic energy change.

### Ideal Gas and Specific Heat

### Ideal Gas and Specific Heat

1.) If the initial volume of an ideal gas is 1.) If the initial volume of an ideal gas is compressed to one-half its original volume compressed to one-half its original volume and twice its original temperature, the and twice its original temperature, the pressure is?

2.) A rigid vessel initially contains helium at 2.) A rigid vessel initially contains helium at 105kPaa and 15

105kPaa and 15⁰C⁰C. Two kilograms of helium. Two kilograms of helium are then added to the contents so that the are then added to the contents so that the final pressure and temperature are 200kPaa final pressure and temperature are 200kPaa and 20

and 20⁰C⁰C. Determine. Determine

a) the volume of the vessel; a) the volume of the vessel; b) the final mass of helium. b) the final mass of helium.

3.) A rigid vessel initially contains hydrogen 3.) A rigid vessel initially contains hydrogen at 200kPaa and 20

at 200kPaa and 20⁰C⁰C. Two kilograms of . Two kilograms of hydrogen are then pumped out so that the hydrogen are then pumped out so that the final pressure and temperature is at 105kPaa final pressure and temperature is at 105kPaa and 15

and 15⁰C⁰C. Determine. Determine a) the final mass of

a) the final mass of hydrogen;hydrogen; b) the volume of the vessel. b) the volume of the vessel.

4.) A 1500L tank contains nitrogen at a 4.) A 1500L tank contains nitrogen at a pressure of 400kPag and a temperature of pressure of 400kPag and a temperature of 320K. Later, because of a leak, it was found 320K. Later, because of a leak, it was found that the gage pressure has dropped to that the gage pressure has dropped to 320kPag and the temperature has decreased 320kPag and the temperature has decreased to 300K; determine

to 300K; determine

a) the initial mass of nitrogen; a) the initial mass of nitrogen; b) the remaining nitrogen;

b) the remaining nitrogen;

c) the amount of nitrogen that has leaked c) the amount of nitrogen that has leaked out.

5.) A bicycle pump is full of air at 5.) A bicycle pump is full of air at atmospheric press

atmospheric pressure. The length ure. The length of stroke of of stroke of the pump is 45cm. At what part of the stroke the pump is 45cm. At what part of the stroke does the air begin to enter the tire in which does the air begin to enter the tire in which the gage pressure is 310kPag? Assume the gage pressure is 310kPag? Assume compression is isothermal.

6.) An air bubble rises from the bottom of a6.) An air bubble rises from the bottom of a

well where the temperature is 27

well where the temperature is 27⁰C⁰C. Find the. Find the percentage increase in volume of the bubble percentage increase in volume of the bubble if the depth of the well is 5m. Atmospheric if the depth of the well is 5m. Atmospheric pressure is 101.528kPaa.

pressure is 101.528kPaa.

7.) A 15cm diameter x 100cm length 7.) A 15cm diameter x 100cm length cylindrical steel vessel contained nitrogen at cylindrical steel vessel contained nitrogen at 1315kPag and 28

1315kPag and 28⁰C⁰C. After some of the. After some of the nitrogen was used the pressure and nitrogen was used the pressure and temperature dropped to 480kPag and 22

temperature dropped to 480kPag and 22⁰C⁰C.. a) What proportion of nitrogen was used?

a) What proportion of nitrogen was used?

b) What volume would the used nitrogen b) What volume would the used nitrogen occupy at 1atm and 15.5

8.) A 0.8m diameter sphere contains helium 8.) A 0.8m diameter sphere contains helium at 20bar and 28

at 20bar and 28⁰C⁰C. How many cylindrical. How many cylindrical drums 12cm in diameter and 70cm long, drums 12cm in diameter and 70cm long, which is initially devoid of any gas, can be which is initially devoid of any gas, can be filled to a pressure of 3bar at 18

filled to a pressure of 3bar at 18⁰C?⁰C? AssumeAssume the helium in the sphere remains at 28

9.) Complete the following ideal gas table: 9.) Complete the following ideal gas table:

10.) 8kg of a gas, R=280J/kg.K and 10.) 8kg of a gas, R=280J/kg.K and C

C_{v}_{v}=0.78kJ/kg.K undergo a reversible non-=0.78kJ/kg.K undergo a reversible
non-flow constant pressure process from
flow constant pressure process from
V

V_{1}_{1}=1.2m=1.2m33_{, }_{, P}_{P}
1

1=700kPaa to a state where=700kPaa to a state where

T

T_{2}_{2}=480=480⁰C⁰C. Find. Find

a)ΔU,

a)ΔU, ΔH,ΔH, Q, WQ, W_{nf }_{nf };;

b) if the process has been a reversible steady b) if the process has been a reversible steady flow type with

11.) A 0.064kg of octane vapor (MW=114) is 11.) A 0.064kg of octane vapor (MW=114) is mixed with 0.91kg of air (MW=29) in the mixed with 0.91kg of air (MW=29) in the manifold engine. The total pressure of the manifold engine. The total pressure of the manifold engine is 86.1kPa and the manifold engine is 86.1kPa and the temperature is 290K. Assume octane behaves temperature is 290K. Assume octane behaves ideally. What is the partial pressure of the air ideally. What is the partial pressure of the air in the mixture in kPa?

12.) 5kg of O

12.) 5kg of O_{2}_{2}, 0.5kg of CO, 0.5kg of CO_{2}_{2} and 8.5kg of Nand 8.5kg of N_{2}_{2}
are mixed at constant temperature until the
are mixed at constant temperature until the
mixture pressure is constant at 690kPaa.
mixture pressure is constant at 690kPaa.
Determine

Determine

a) the partial pressure of each gas; a) the partial pressure of each gas;

b) the molecular weight of the mixture; and b) the molecular weight of the mixture; and c) the gas constant of

13.) It is desired to produce a gas mixture 13.) It is desired to produce a gas mixture containing 35% by volume of CO

containing 35% by volume of CO_{2}_{2} and 65% byand 65% by
volume of oxygen. If there is 1.4kg of CO

volume of oxygen. If there is 1.4kg of CO_{2}_{2} inin
the mixture, find

the mixture, find a) mass of O

a) mass of O_{2}_{2} in the mixture;in the mixture;
b) the gas constant of

14.) CHALLENGE! A valve joins a two 14.) CHALLENGE! A valve joins a two compartment adiabatic tank. 0.75 kg of compartment adiabatic tank. 0.75 kg of nitrogen dioxide at 4500kPaa and 400K is nitrogen dioxide at 4500kPaa and 400K is contained in one compartment while 0.45kg contained in one compartment while 0.45kg of air at 550kPaa and 300K is contained in of air at 550kPaa and 300K is contained in the other compartment. The valve is opened the other compartment. The valve is opened and the gasses mix. Determine

and the gasses mix. Determine a) the gas constant for the

a) the gas constant for the mixture;mixture;

b) the final temperature and pressure of the b) the final temperature and pressure of the mixture.