Civil Engineering Chapter 9 Rotational Kinetic Energy Yet Another Massdependent Engineering Quantity Object Having Mass Moment

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9.32 Rotational kinetic energy is yet another mass-dependent engineering quantity. An

object having a mass moment of inertia I and rotating with angular speed of



(rad/s) has a rotational kinetic energy, which is equal to ½ I



2. Determine the

rotational kinetic energy of a steel shaft that is 4 ft long and has diameter of 2 in,

and is rotating at an angular speed of 100 rpm. Express your answer in SI, BG,

and U.S. Customary units.

SOLUTION

9.33 Determine the change in mass moment of inertia of an object that could be

modeled as a point mass m when its distance from a center of rotation is doubled.

SOLUTION

9.34 Convert the density, specific gravity, and specific weight data in Table 9.1 from

SI units to U.S. Customary units. Present your solution in a tabular form similar to

Table 9.1. Do you need to change the values of specific gravity?

85

in whole or in part.

SOLUTION

You don’t need to change the specific gravity values, since they are unitless.

Gravity

Weight

304)

(mahogany)

550

0.55

5,400

34.27

Wood (oak) 750

0.75

7,360

46.73

9.35 Convert the density, specific gravity, and specific weight data in Table 9.1 from

SI units to British Gravitational units. Present your solution in a tabular form

similar to Table 9.1. Do you need to change the values of specific gravity?

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SOLUTION

You don’t need to change the specific gravity values, since they are unitless.

Material Density

Specific

Gravity

Specific

Weight

Density Specific

Weight

(kg/m3) (N/m3) (slugs/ft3) (lbf/ft3)

Aluminum 2,740

2.74

26,880

5.30

170.7

Steel (mild) 7,830

7.83

76,810

15.15

487.8

Steel (stainless

304)

7,860

7.86

77,110

15.21

489.7

Wood (ash) 690

0.69

6,770

1.34

43.0

Wood (mahogany) 550

0.55

5,400

1.06

34.3

9.36 A plugged dishwasher sink with the dimensions of 14 in × 16 in × 6 in is being

filled with water from a faucet with an inner diameter of 1 in. If it takes 220

seconds to fill the sink to its rim, estimate the mass flow of water coming out of

the faucet.

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SOLUTION

s

slugs

0.007

s

kg

0.1



9.37 Imagine the plug of the sink described in Problem 9.36 leaks. If it now takes 250

seconds to fill the sink to its rim, estimate the mass-flow rate of the leak.

SOLUTION

s

lb

s

9.38 The tank shown in the accompanying figure is being filled by Pipes 1 and 2. If the

water level is to remain constant, what is the mass-flow rate of water leaving the

tank at Pipe 3? What is the average velocity of the water leaving the tank?

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SOLUTION

Assume constant water density.

12

4

12

4

12

4

9.39 Imagine, the water level in the tank described in Problem 9.38 rises at a rate of 0.1

in/s. Knowing the diameter of the tank is 6 in., what is the average velocity of the

water leaving the tank? Express your answer in in/s, ft/s, and m/s.

time

3tan21 Q

time

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in whole or in part.

Solving for Q3 and V3, we get:

Q3 = 0.0343 ft3/s and V3= 2.79 ft/s = 33.48 in/s = 0.85 m/s

9.40 The density of air at a city (such as San Diego) located at sea level is 1.225 kg/m3,

while for a city (such as Denver) located at high altitude is 1.048 kg/m3. Consider

two auditoriums, each with dimensions of 100 ft ×150 ft ×20 ft, one located in

San Diego, and the other in Denver. Calculate the mass of air for each auditorium.

Express your answer in kg, lbm, and slugs.

m

9.41 A rectangular duct with dimensions of 12 in. × 14 in. delivers conditioned air with

a density of 1.2 kg/m3 to a room at a rate of 1200 ft3/min. What is the mass-flow

rate of air in lbm/h? What is the average air speed in the duct? Express your

answer in m/s and ft/s.

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9.42 A rubber balloon has a mass of 10 grams. The balloon is filled with air and forms

a shape that may be approximated as a sphere with a diameter of 1.5 ft. What is

the total mass the balloon? What would be the total mass of the balloon, if it is

filled with helium instead? Express your answers in grams.

SOLUTION

9.43 A typical household of 4 people consume approximately 80 gallons of water per

day. Express the annual consumption rate of a city with a population of 100,000

people. Express your answer in slugs per year, lbm per year, and kg per year.

SOLUTION

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9.44 Lake Mead of Hoover Dam, the largest man-made lake in the United States,

contains 28,537,000 acre-foot (an acre-foot is the amount of water required to

cover 1 acre to a depth of 1 foot). Express the mass of the water volume in kg and

lbm.

9.45 Air with density of 0.45 kg/m3enters an experimental jet engine at rate of 180 m/s.

The inlet area of the engine is 5.0 ft2. After fuel is burned, the air and combustion

byproducts leave the engine with a velocity of 650 m/s through and outlet area of

4.0 ft2. What is the average density of the gas exiting the engine? Express your

answer in kg/m3, slugs/ft3, and lbm/ft3.

SOLUTION

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9.46 In a food processing (drying) application, air (



= 1.10 kg/m3, V = 10 ft/min)

enters a chamber through a duct with dimensions of 20 in. × 18 in. and leaves (



=

1.10 kg/m3) through a ductwork with dimensions of 14 in. × 16 in. What is the

average air speed in the exit duct? Express your answer in ft/min and m/s.

SOLUTION

9.47 To measure the fuel consumption of an experimental lawn mower, fuel is drawn

from a tank that is resting on a scale as shown in the figure. The tank and the fuel

have an initial total mass of 10 kg. If the mass scale shows a value of 9.45 kg after

30 minutes, what is the fuel consumption of the lawn mower in gallons per hour?

SOLUTION

9.48 In a water bottling process, one-liter bottles are filled through a system that

provides filtered water to each bottle at rate of 0.7 lbm/s. How long would it take

to fill a bottle? How many bottles can be filled in one hour, if the system can fill

20 bottles simultaneously with a required time of 3 seconds to move away the

filled bottles and bring in the new batch of empty bottles?

SOLUTION

h

bottles

20

seconds

6.14

9.49 Water is available at a rate of 400 gallons/min to a small apartment complex,

consisting of 4 units. If at a given time, units 1, 2, and 3 are consuming 18 lbm/s,

14 lbm/s, 16 lbm/s, respectively, how much water is available to unit 4? Express

your answer in gallons/min, ft3/s, m3/s and lbm/s, and kg/s.

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in whole or in part.

The amount of water available to unit – 4 = 54.7 gallons/min = 0.122 ft3/s = 0.00345

m3/s = 7.6 lbm/s = 3.45 kg/s

9.51 In the United States, every kilowatt-hour of electricity generated in a power plant

produces approximately 1.7 pounds of CO2 on average. Therefore, when you

watch a 46-inch-LCD TV that consumes 250 watts (W) for 4 hours, you consume

1000 watt-hours (Wh) or 1 kilowatt-hour (kWh) of energy. Calculate the amount

(in pounds) of CO2 released into the atmosphere annually due to watching TV.

Assume you leave your TV on (whether you watch it or not) for 4 hours every

night for 200 nights.