The unit for all types of power 4 All of the above

h. What force may be needed to lift a heavy suitcase? 1. 24 N

2. 250 N 3. 25 kN 4. 250 kN

Section 2.2 Conversion of Units

*2.2.1. Carry out the following conversions:

a. How many m3 are there in 1.00 (mile)3? b. How many gal/min correspond to 1.00 ft3/s? 2.2.2. Convert

*a. 0.04 g/[(min)(m3)] to lb_m/[(hr)(ft3)] *b. 2 L/s to ft3/day

**c. to all SI units

*2.2.3. Convert the following: a. 60.0 mi/h to ft/s b. 50.0 lb/in.2 to kg/m2 c. 6.20 cm/hr2 to nm/s2

**2.2.4. A technical publication describes a new model 20 hp Stirling (air cycle) engine that drives a 68 kW generator. Is this possible?

**2.2.5. Your boss announced that the speed of the company Boeing 737 is to be cut from 525 mi/hr to 475 mi/hr to “conserve fuel,” thus cutting consumption from 2200 gal/hr to 2000 gal/hr. How many gallons are saved in a 1000 mi trip?

**2.2.6. From Parade magazine (by Marilyn Vos Savant, August 31, 1997, p. 8): “Can you help with this problem? Suppose it takes one man 5 hours to paint a house, and it takes another man 3 hours to paint the same house. If the two men work together, how many hours would

it take them? This is driving me nuts.”

**2.2.7. Two scales are shown in Figure P2.2.7, a balance (a) and a spring scale (b). In the

balance, calibrated weights are placed in one pan to balance the object to be weighed in the other pan. In the spring scale, the object to be weighed is placed on the pan and a spring is compressed that moves a dial on a scale in kilograms.

Figure P2.2.7

State for each device whether it directly measures mass or weight. Underline your answer. State in one sentence for each the reason for your answer.

**2.2.8. In the American Engineering system of units, the viscosity can have the units of (lb_f)

(h)/ft2, while in a handbook the units are (g)/[(cm)(s)]. Convert a viscosity of 20.0 (g)/[(m) (s)] to the given American Engineering units.

**2.2.9. Thermal conductivity in the American Engineering system of units is

Determine the conversion factor to convert from AE units to the following units:

***2.2.10. Water is flowing through a 2-in.-diameter pipe with a velocity of 3 ft/s. a. What is the kinetic energy of the water in (ft)(lb_f)/lb_m?

b. What is the flow rate in gallons per minute?

****2.2.11. Consider water pumped at a rate of 75 gal/min through a pipe which undergoes a 100 ft elevation increase by a 2 hp pump. The rate energy input from the pump that goes into

heating the water is approximately equal to the rate of energy input from the pump minus the rate of potential energy generated by pumping the water up the elevation change (m′gh, where m′ is the mass flow rate of water and h is the elevation change). Estimate the rate of energy input for heating the water for this case in British thermal units per hour.

**2.2.12. What is meant by a scale that shows a weight of “21.3 kg”?

***2.2.13. A tractor pulls a load with a force equal to 800 lb (4.0 kN) with a velocity of 300 ft/min (1.5 m/s). What is the power required using the given American Engineering system data? The SI data?

***2.2.14. What is the kinetic energy of a vehicle with a mass of 2300 kg moving at the rate of 10.0 ft/s in British thermal units?

maximum velocity the pallet attains before hitting the ground is 6 ft/s. How much kinetic energy does the pallet have in (ft)(lb_f) at this velocity?

***2.2.16. Calculate the protein elongation (formation) rate per mRNA per minute based on the following data:

a. One protein molecule is produced from x amino acid molecules.

b. The protein (polypeptide) chain elongation rate per active ribosome uses about 1200 amino acids/min.

c. One active ribosome is equivalent to 264 ribonucleotides. d. 3x ribonucleotides equal each mRNA.

Messenger RNA (mRNA) is a copy of the information carried by a gene in DNA and is involved in protein synthesis.

Section 2.3 Dimensional Consistency

*2.3.1. The density of a certain liquid is given an equation of the following form: ρ = (A + BT)eCP

where ρ = density (g/cm3) T = temperature (°C) P = pressure (atm)

For this equation to be dimensionally consistent, what are the units of A, B, and C? *2.3.2. Explain in detail whether the following equation for flow over a rectangular weir is

dimensionally consistent. (This is the modified Francis formula.)

where q = volumetric flow rate (ft3/s) L = crest height (ft)

h₀ = weir head (ft)

g = acceleration of gravity (32.2 ft/s2)

**2.3.3. In an article on measuring flows from pipes, the author calculated q = 80.8 m3/s using the formula

where q = volumetric flow rate (m3/s) C = dimensionless coefficient (0.6) A₁ = cross-sectional area 1 (m2) A₂ = cross-sectional area 2 (m2) V = specific volume (10–3 m3/kg) P = pressure p₁ – p₂ = 50 kPa

g = acceleration of gravity (9.80 m/s)

Was the calculation correct? (Answer yes or no and explain briefly the reasoning underlying your answer.)

***2.3.4. Leaking oil tanks have become such an environmental problem that the federal

government has implemented a number of rules to reduce the problem. A flow rate from a leak from a small hole in a tank can be predicted from the following relation:

where Q is the leakage rate (gal/min)

S is the cross-sectional area of the hole causing the leak (in.2)

Δp is the pressure drop between the inside of the tank opposite the leak and the atmospheric pressure (psi)

ρ is the fluid density (lb/ft3)

To test the tank, the vapor space is pressurized with N₂ to a pressure of 23 psig. If the tank is filled with 73 in. of gasoline (sp. gr. = 0.703) and the hole is ¼ in. in diameter, what is the value of Q (in cubic feet per hour)?

***2.3.5. A relation for a dimensionless variable called the compressibility (z), which is used to describe the pressure-volume-temperature behavior for real gases, is

z = 1 + Bρ + Cρ2 + Dρ3

where ρ is the density in g mol/cm3. What are the units of B, C, and D?

Convert the coefficients in the equation for z so that the density can be introduced into the equation in the units of lb_m/ft3 thus:

z = 1 + B* ρ* + C*(ρ*)2 + D*(ρ*)3

ρ* is in lb_m/ft3. Give the units for B*, C*, and D*, and give the equations that relate B* to B, C* to C, and D* to D.

**2.3.6. The velocity in a pipe in turbulent flow is expressed by the following equation:

where τ is the shear stress in N/m2 at the pipe wall ρ is the density of the fluid in kg/m3

u is the velocity in m/s k is a coefficient

You are asked to modify the equation so that the shear stress can be introduced in the units of τ which are lb_f/ft2, and the density ρ′ for which the units are lb/ft3 so that the velocity u comes out in the units of ft/s. Show all calculations, and give the final equation in terms of u, τ, and ρ′ so a reader will know that American Engineering units are involved in the equation.

transfer between a pure saturated vapor and a colder surface:

where h is the mean heat transfer coefficient, Btu/[(hr)(ft2)(°F)] k is the thermal conductivity, Btu/[(hr)(ft)(°F)]

ρ is the density in lb/ft3

g is the acceleration of gravity, 4.17 × 108 ft/(hr)2 λ is the enthalpy change of evaporation in Btu/lb L is the length of tube in ft

m is the viscosity in lb_m/[(hr)(ft)] ΔT is a temperature difference in °F

What are the units of the constant 0.943?

****2.3.8. The efficiency of cell growth in a substrate in a biotechnology process was given in a report as

In the notation table

η is the energetic efficiency of cell metabolism (energy/energy)

is the cell yield, carbon basis (cells produced/substrate consumed)

γ_b is the degree of reductance of biomass (available electron equivalents/g mole carbon, such as 4.24 e– equiv./mol cell carbon)

is the biomass heat of combustion (energy/available electron equiv.) ΔH_cat is the available energy from catabolism (energy/mole substrate carbon)

Is there a missing conversion factor? If so, what would it be? The author claims that the units in the numerator of the equation are (mol cell carbon/mol substrate carbon) (mol available e-/mol cell carbon) (heat of combustion/mol available e-). Is this correct? ****2.3.9. The Antoine equation, which is an empirical equation, is used to model the effect of

temperature on the vapor pressure of a pure component. The Antoine equation is given by

where p* is the vapor pressure, T is the absolute temperature, and A, B, and C are empirical constants specific to the pure component and the units used for the vapor pressure and temperature. Determine under what conditions this equation will be dimensionally consistent.

**2.3.10. A letter to the editor says: “An error in units was made in the article ‘Designing Airlift Loop Fermenters.’ Equation (4) is not correct.”

Is the author of the letter correct? (f is dimensionless.) Section 2.4 Significant Figures

*2.4.1. If you subtract 1191 cm from 1201 cm, each number with four significant figures, does the answer of 10 cm have two or four (10.00) significant figures?

*2.4.2. What is the sum of 3.1472 32.05 1234 8.9426 0.0032 9.00

to the correct number of significant figures?

**2.4.3. Suppose you make the following sequence of measurements for the segments in laying out a compressed air line:

4.61 m 210.0 m 0.500 m

What should be the reported total length of the air line?

**2.4.4. Given that the width of a rectangular duct is 27.81 cm, and the height is 20.49 cm, what is the area of the duct with the proper number of significant figures?

**2.4.5. Multiply 762 by 6.3 to get 4800.60 on your calculator. How many significant figures exist in the product, and what should the rounded answer be?

***2.4.6. Suppose you multiply 3.84 times 0.36 to get 1.3824. Evaluate the maximum relative error in (a) each number and (b) the product. If you add the relative errors in the two numbers, is the sum the same as the relative error in their product?

Section 2.6 The Mole and Molecular Weight