Civil Engineering Chapter 8 Time And Timerelated Variables Engineering Create Calendar Showing The Beginning And

47

Chapter 8: Time and Time-Related Variables in Engineering

8.1 Create a calendar showing the beginning and the end of daylight savings time for years

2025-2031.

Year Daylight Savings Time

Begins at 2:00

A.M

.

Daylight Savings Time

Ends at 2:00

A.M

.

2025

2026

2027

2028

2029

2030

2031

8.10 Convert the following speed limits from miles per hour (mph) to kilometers per hour

(km/h), and from feet per second (ft/s) to meters per second (m/s). Think about the

relative magnitude of values as you go from mph to ft/s, and as you go from km/h to m/s.

You may use Excel to solve this problem.

48

speed limits

(mph)

Speed limits

(km/h)

Speed limit

(ft/s)

Speed limit

(m/s)

15

25

30

35

40

45

55

65

70

8.11 Most car owners drive their cars an average of 12,000 miles a year. Assuming a 20

miles/gallon gas consumption rate, determine the amount of fuel consumed by 150

million car owners on the following time bases:

a. average daily basis

b. average weekly basis

c. average monthly basis

d. average yearly basis

e. over a period of ten years

Express your results in gallons and liters.

49

SOLUTION

a. 12,000 miles/365 days

8.12 Calculate the speed of sound for the U.S. standard atmosphere using, kRTc  where c

represents the speed of sound in m/s, k is the specific heat ratio for air (k = 1.4), and R is

the gas constant for the air (R = 286.9 J/kg·K) and T represents the temperature of the air

in Kelvin. The speed of sound in atmosphere is the speed at which sound propagates

through the air. You may use Excel to solve this problem.

Altitude

(m)

Air Temperature

(K)

Speed of Sound

(m/s)

Speed of Sound

(km/h)

500

284.9

1,000

281.7

2,000

275.2

5,000

255.7

10,000

223.3

15,000

216.7

20,000

216.7

40,000

250.4

50,000

270.7

50

SOLUTION

Altitude

(m)

Air Temperature

(K)

Speed of Sound

(m/s)

Speed of Sound

(km/h)

500 284.9 338 1218

1,000 281.7 336 1211

2,000 275.2 332 1197

8.13 Express Equation (8.5), the traffic density in terms of number of vehicles per mile.

SOLUTION

8.14 Express the angular speed of the earth in rad/s and rpm.

SOLUTION

8.15 What is the magnitude of the speed of a person at the equator due to rotational speed of

the earth?

2

rev 1

h 24













8.18 Determine the speed of a point on the earth surface in ft/s, m/s, mph, km/h. State your

assumptions.

2

rev 1

h 24













52

in part.

m/s 464

s 3600

h 1

km 1

m 1000

h

km

1669 





































V

ft/s 1522

m 1

ft 3.28

s

m

464 

























V

mph 1037

h 1

s 3600

ft 5280

mile 1

s

ft

1522 





































V

8.19 Into how many time zones is the United states and its territories divided into?

8.21 Determine the natural frequency of a pendulum whose length is 15 ft.

SOLUTION

s

29

.

4

T

8.22 Determine the spring constant for Example 8.1 if the system is to oscillate with a natural

frequency of 5 Hz.

SOLUTION

53

in part.

m

k

fn



2

1







  

 





kg 2

N/m

2 Hz5

kg 2

N/m

2

1

Hz5 2kk 



and solving for k, we get

N/cm 19.74N/m 1974



k

8.23 Determine the traffic flow if 100 cars pass a known location during 10 seconds.

10

8.24 A conveyer belt runs on 4-in. drums that are driven by a motor. If it takes 5 s for the belt

to go from zero to the speed of 4 ft/s, calculate the final angular speed of the drum and its

angular acceleration. Assume constant acceleration.

SOLUTION

2

in. 12





54

in part.

change in angular speed

angular accleration

time







2

rad/s 8.4

s

5

rad/s 0 –24

onacceleratiangular 

8.25 Chinook, a military helicopter has two three-blade rotor systems, each turning in opposite

direction. Each blade has a diameter of approximately 41 ft. The blades can spin at

angular speeds of up to 225 rpm. Determine the translational speed of a particle located at

the tip of a blade. Express your answer in ft/s, mph, m/s, and km/h.

SOLUTION

h 1

m 1000

s













8.26 Consider the piping system shown in the accompanying figure. The speed of water

flowing through the 4-in.-diameter section of the piping system is 3 ft/s. What is the

volume flow rate of water in the piping system? Express the volume flow rate in ft3/s,

gpm, and L/s. For the case of steady flow of water through the piping system, what is the

speed of water in the 3-in.-diameter section of the system?

55

SOLUTION

 

in 12

ft 1

in 3

4

flow ofarea sectional–cross

2

average 



























8.27 Consider the duct system shown in the accompanying figure. Air flows through two 8-

in.-by-10-in. ducts that merge into a 18-inch-by-14-inch duct. The average speed of the

air in each of the 8 x 10 duct is 30 ft/s. What is the volume flow rate of air in the 18 × 14

duct? Express the volume flow rate in ft3/s, ft3/min, and m3/s. What is the average speed

of air in the 18 ×14 duct?

SOLUTION

s

in 12

s













56

in part.

s

ft

4.33

s

ft

7.16

s

ft

7.16duct14″x 18″ thein rateflow volumeQ

333

total 

min.

ft

2004

min. 1

s 60

s

ft

4.33Q

33

total 



























s

m

95.0

ft 28.3

m 1

s

ft

4.33Q

3

total 



























ft/s 1.19

in 12

ft 1

in) 14(

in 12

ft 1

in) (18

s

ft

4.33

flow ofarea sectional–cross

Q

3

total

average 

























V

8.28 A car starts from rest and accelerates to a speed of 60 mph in 20 s. The acceleration

during this period is constant. For the next 20 minutes the car moves with the constant

speed of 60 mph. At this time the driver of the car applies the brake and the car

decelerates to a full stop in 10 s. The variation of the speed of the car with time is shown

in the accompanying diagram. Determine the total distance traveled by the car and the

average speed of the car over this distance. Also plot the acceleration of the car as a

function of time.

SOLUTION

57

in part.

During the next 20 minutes the car moves with a constant speed of 60 mph and the

distance traveled during this period is

 

ft 105600

mile 1

ft 5280

s 3600

h 1

h

miles

60s 1200

2





































d

Because the car decelerates at a constant rate from a speed of 60 mph to 0, the average

speed of the car during the last 10 seconds is also 30 mph, and the distance traveled

during this period is

 

ft 440

mile 1

ft 5280

s 3600

h 1

h

miles

30s 10

3





































d

The total distance traveled by the car is

miles 20.25 ft 106920440105600880

321  dddd

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

mph 59.3ft/s 86.9

1230

106920

time

traveleddistance

average V

To plot the acceleration of the car as a function of time, first we need to compute the

acceleration during the first 20 seconds, the next 20 minutes, and the last 10 seconds.

During the initial 20 seconds, the acceleration of the car is

2

ft/s 4.4

s

20

ft/s 88

onaccelerati 

Note during this period, the speed of the car changes from 0 to ft/s 88 mph 60



V.

During the next 20 minutes the car moves with constant speed of 60 mph and therefore

acceleration is zero.

During the last 10 seconds the car decelerates at the following rate.

2

ft/s 8.8

s

10

ft/s 88

iondeccelerat 

Acceleration (ft/s

2

)

59

8.31 On a gusty windy day, the blades of a wind turbine are turning at a rate of 200

revolutions per minute, when suddenly brakes are applied to stop the turbine to avoid

failure. If the brakes cause a deceleration of 2 rad/s2, how long would it take for the

blades of the wind turbine to come to rest?

SOLUTION

8.32 A plugged dishwasher sink with the dimensions of 2 ft × 1.5 ft × 1 ft is being filled with

water from a faucet with an inner diameter of 1 in. If it takes 40 seconds to fill the sink to

its rim, estimate the volumetric flow of water coming out of the faucet. What is the

average velocity of water coming out of the faucet?

SOLUTION





12

4

s

average

8.33 Imagine, the plug in the sink described in Problem 8.32 leaks. If it now takes 45 seconds

to fill the sink to its rim, estimate the volumetric flow rate of the leak.

SOLUTION