Civil Engineering Chapter 8 Sink Qfaucet Qleak Qleak Qleak Rectangular Duct With Dimensions Delivers Conditioned Air

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8.34 A rectangular duct with dimensions of 12 in × 14 in delivers conditioned air to a room at

a rate of 1000 ft3/min. What should be the size of a circular duct if the average air

velocity inside the duct is to remain the same?

SOLUTION

Assume constant air density.

61

8.35 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 volumetric flow rate of water leaving the tank at

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

SOLUTION

Assume constant water density.









flow ofarea sectional–cross velocityaveragerateflow volumeQ



8.36 Imagine that the water level in Problem 8.35 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?

SOLUTION

8.37 If it takes a bicyclist 25 seconds to reach a speed of 10 mph from rest, what is her

acceleration? For the next 10 minutes, she moves at the constant speed of 10 mph, and at

this time, she applies her brakes, and the bicycle decelerates to a full stop in 5 seconds.

What is the total distance travelled by the bicyclist? Determine the average speed of the

cyclist during the first 25 seconds, 625 seconds, and 630 seconds. State your

assumptions.

63

in part.

 

ft 66.36

mile 1

ft 5280

s 3600

h 1

h

miles

55s

3





































d

The total distance traveled by the bicycle is

miles 1.71 ft 902066.36880033.183

321  dddd

And finally, the average speed of the bicyclist for the entire duration of travel is

average

distance traveled 9020 14.32 ft/s 9.76 mph

time 630

V   

8.38 An object is dropped from the roof of a high-rise building, a distance of 450 ft. Prepare a

table similar to Table 8.3 showing speed and acceleration of the object, and the distanced

travelled by the object as a function of time.

SOLUTION

Time (s)

Acceleration

(ft/s2)

speed

(ft/s)

distance

(ft)

1 32.2 32.2 16.1

3 32.2 96.6 144.9

5 32.2 161.0 402.5

8.39 Solve Problem 8.38 for a situation in which the object is given an initial vertical upward

velocity of 4 ft/s. Again, prepare a table similar to Table 8.3 showing the speed and

acceleration of the object, and the distanced travelled by the object as a function of time.

SOLUTION

Time

(s)

Acceleration

(ft/s2)

speed

(ft/s)

distance

travelled (ft)

0

32.2

4.0

0

Moves upward,

reaches the

highest point; stops and

moving downward

2.124

32.2

64.4

64.7

3.124

32.2

96.6

145.2

4.124

32.2

128.8

257.9

5.124

32.2

161.0

402.8

5.404

32.2

170.0

449.1

Note the difference between position and actual distance travelled.

8.40 Determine the natural frequency of the system given in Example 8.1, if its mass is

doubled.

SOLUTION

8.41 The period of oscillation for a pendulum on Earth is 2 seconds. If the given pendulum

oscillates with a period of 4.9 seconds on the surface of the Moon, what is the

acceleration due to gravity on the Moon’s surface? Express your answer in both SI and

U.S. Customary units.

65

For earth:

m

2 2 L

s





8.42 What is the period of oscillation of the pendulum given in Problem 8.41 on Mar’s

surface? (gEarth = 9.81 m/s2 and gMars = 3.70 m/s2)

SOLUTION

L

T



2

8.43 The power to an electric motor running at a constant speed of 1600 rpm is suddenly

turned off. It takes 10 seconds for the motor to come to rest. What is the deceleration of

the motor? How many turns does the motor make before it stops. State your assumptions.

SOLUTION

s

1

2

rev 133.4rad 838s) )(10

s

2

s

8.44 The 2013 world record for the 100-m sprint is 9.75 seconds and belongs to an American

runner named Tyson Gay. Assuming constant acceleration, determine the speed of Mr.

Gay at distances of 10 m, 20 m, 30 m, . . , 80 m, 90 m, and 100 m.

SOLUTION

2

s

distance (m) speed (m/s)

10 6.48

30 11.22

50 14.49

70 17.15

90 19.44

8.45 The 2013 women’s pole vault world record of 4.89 m belongs to Yelena Isinbayeva of

Russia. If the pole vault mat has the dimensions of 6.0 m × 8.0 m × 0.8 m, what is the

vertical speed of the vaulter right before she strikes the mat?

8.46 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 gallons per year, ft3 per year, liters per year, and m3 per year.

SOLUTION

galllons

gallons

8.47 The American Society of Heating, Ventilating, and Air Conditioning Engineers

(ASHRAE) sets the standard for outdoor air requirement for ventilation purposes. For

example, for a gymnasium, an outdoor air requirement of 20 cfm (cubic feet per minute)

per person is required. What is the total volume of the outdoor air that must be introduced

into a gym during a 12-hour period, if on average 30 people are using the gym every

minute? Express your answer in ft3, liters, and m3.

3

ft

1

68

8.48 The design fluid (typically water + antifreeze) flow rate through a solar hot-water heater

system is 0.02 gpm/ft2. If a system runs continuously for 3 hours and makes use of two

solar panels (each 4 ft × 8 ft), what is the total volume of the fluid that goes through the

collector during this period. Express your answer in gallons, ft3, liters, and m3.

SOLUTION

8.49 Assuming that a large family uses a dishwasher that uses 10 gallons (~35 liters) of water

per wash three times a week, what is the total amount of water consumed by the

dishwater in a year?

SOLUTION

8.50 An old showerhead delivers approximately 3 gallons (~12 liters) of water per minute.

Assuming that a person showers twice a day for 5 minutes each time, what is the total

amount of water that is consumed for this activity annually?

SOLUTION

8.52 A car-wash system consume 60 gallons (~225 liters) water per wash. Assuming that a

person washes her car once every week, what is the total amount of water consumed

annually by this activity?

69

SOLUTION

8.56 According to the USGS in 2010, about 355 billion gallons of water per day were

consumed to address various needs in the United States. Show that this volume is equal to

397,000 thousand acre-feet per year. (Note: An acre-foot is the amount of water required

to cover 1 acre to a depth of 1 ft, 1 acre is equal to 43,560 ft2, and 1 ft3 = 7.48 gallons.)

SOLUTION

8.57 Convert the results of Examples 8.7–8.11 from US Customary units to SI units.

70

SOLUTION

8.58 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 this water volume in gallons and m3.

SOLUTION

8.59 Within the next 5 to 10 years, wind turbines with rotor diameters of 180 m are anticipated

to be developed and installed in Europe. If the blades of such turbine turn at a rate of 5

revolutions per minute, what is the speed of a point located at a tip of a blade? Express

your answer in ft/s, m/s, km/h, and mph.

71

SOLUTION