Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 7, Problem 125RQ
To determine

The amount of oil and money, a family of four will save per year by replacing the standard shower heads by the low-flow ones.

Expert Solution & Answer
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Explanation of Solution

Given:

The initial volume of the low-flow shower head (ν1) is 13.3L/min.

The final volume of the low-flow shower head (ν2) is 10.5L/min.

The time (t) is 6 min.

The number person in family (n) is 4.

The density of water (ρwater) is 1kg/L

The specific heat of water (cp) is 4.18kJ/kg°C.

The initial temperature of the low-flow shower head (T1) is 15°C.

The final temperature of the low-flow shower head (T2) is 42°C.

The efficiency of the fuel in the low-flow shower head (ηfuel) is 0.65.

The heating value of fuel (HV) is 146,300kJ/gal.

The unit cost of fuel is $2.80/gal

Calculation:

Calculate the rate of water saved volume of the low-flow shower head a family of four will save per year.

  ν˙saved=[(ν1ν2)×(t/(personday))×(n)×(number of days per year)]

  ν˙saved=[(13.310.5)L/min×(6min/(personday))×(4persons)×(365days/year)]=[2.8L/min×(6min/(personday))×(4persons)×(365days/year)]=24,528L/year

Calculate the mass flow rate of water of the low-flow shower head.

  m˙saved=ρwater×ν˙saved

  m˙saved=(1kg/L)×(24,528L/year)=24,528kg/year

Calculate the amount of energy saved in the low-flow shower head.

  Esaved=(m˙watercpΔT)=m˙watercp(T1T2)

  Esaved=(24,528kg/year)×(4.18kJ/kg°C)×(42°C15°C)=(24,528kg/year)×(4.18kJ/kg°C)×(27°C)=2768230kJ/year

Calculate the amount fuel saved in the low-flow shower head.

  Fuelsaved=Esaved(ηfuel)(HV)

  Fuelsaved=(2768230kJ/year)(0.65)×(146,300kJ/gal)=(2768230kJ/year)(0.65)×(146,300kJ/gal)=(2768230kJ/year)(95095kJ/gal)=29.1gal/year

Thus, the amount of oil, a family of four will save per year by replacing the standard shower heads by the low-flow ones is 29.1gal/year_.

Calculate the amount of money saved in the low-flow shower head.

  Moneysaved=(fuel saved)×(unit cost of fuel)

  Moneysaved=(29.1gal/year)×($2.80/gal)=$81.5/year

Thus, the amount of money, a family of four will save per year by replacing the standard shower heads by the low-flow ones is $81.5/year_.

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Chapter 7 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 7 - Does a heat engine that has a thermal efficiency...Ch. 7 - Prob. 12PCh. 7 - Are the efficiencies of all the work-producing...Ch. 7 - Consider a pan of water being heated (a) by...Ch. 7 - A steam power plant receives heat from a furnace...Ch. 7 - Prob. 16PCh. 7 - Prob. 17PCh. 7 - The thermal efficiency of a general heat engine is...Ch. 7 - Prob. 19PCh. 7 - Prob. 20PCh. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - Prob. 23PCh. 7 - In 2001, the United States produced 51 percent of...Ch. 7 - Prob. 25PCh. 7 - Prob. 26PCh. 7 - Prob. 27PCh. 7 - Prob. 28PCh. 7 - Prob. 29PCh. 7 - Prob. 30PCh. 7 - Prob. 31PCh. 7 - Prob. 32PCh. 7 - Prob. 33PCh. 7 - Prob. 34PCh. 7 - Prob. 35PCh. 7 - What is the Clausius expression of the second law...Ch. 7 - Show that the Kelvin–Planck and the Clausius...Ch. 7 - Prob. 38PCh. 7 - Prob. 39PCh. 7 - A residential heat pump has a coefficient of...Ch. 7 - Prob. 41PCh. 7 - Prob. 42PCh. 7 - Prob. 43PCh. 7 - A household refrigerator that has a power input of...Ch. 7 - Prob. 45PCh. 7 - Prob. 46PCh. 7 - Prob. 47PCh. 7 - Prob. 48PCh. 7 - A household refrigerator runs one-fourth of the...Ch. 7 - A heat pump used to heat a house runs about...Ch. 7 - Prob. 51PCh. 7 - Consider a building whose annual air-conditioning...Ch. 7 - Prob. 53PCh. 7 - Prob. 54PCh. 7 - Prob. 55PCh. 7 - Prob. 56PCh. 7 - Prob. 57PCh. 7 - Why does a nonquasi-equilibrium compression...Ch. 7 - Prob. 59PCh. 7 - Prob. 60PCh. 7 - Prob. 61PCh. 7 - Prob. 62PCh. 7 - Prob. 63PCh. 7 - Prob. 64PCh. 7 - Prob. 65PCh. 7 - Prob. 66PCh. 7 - Prob. 67PCh. 7 - Is there any way to increase the efficiency of a...Ch. 7 - Prob. 69PCh. 7 - Prob. 70PCh. 7 - Prob. 71PCh. 7 - Prob. 72PCh. 7 - Prob. 73PCh. 7 - Prob. 74PCh. 7 - Prob. 75PCh. 7 - An inventor claims to have devised a cyclical...Ch. 7 - A heat engine receives heat from a heat source at...Ch. 7 - In tropical climates, the water near the surface...Ch. 7 - A well-established way of power generation...Ch. 7 - Prob. 80PCh. 7 - Prob. 81PCh. 7 - Prob. 82PCh. 7 - Prob. 83PCh. 7 - Prob. 84PCh. 7 - Prob. 85PCh. 7 - Prob. 86PCh. 7 - Prob. 87PCh. 7 - Prob. 88PCh. 7 - Prob. 89PCh. 7 - Prob. 90PCh. 7 - Prob. 91PCh. 7 - Prob. 92PCh. 7 - Prob. 93PCh. 7 - Prob. 94PCh. 7 - Prob. 95PCh. 7 - Prob. 96PCh. 7 - Prob. 97PCh. 7 - Prob. 98PCh. 7 - Prob. 99PCh. 7 - Prob. 100PCh. 7 - Prob. 101PCh. 7 - Prob. 102PCh. 7 - Prob. 103PCh. 7 - Prob. 104PCh. 7 - Prob. 105PCh. 7 - Prob. 106RQCh. 7 - Prob. 107RQCh. 7 - Prob. 108RQCh. 7 - Prob. 109RQCh. 7 - Prob. 110RQCh. 7 - Prob. 111RQCh. 7 - Prob. 112RQCh. 7 - Prob. 114RQCh. 7 - Prob. 115RQCh. 7 - Prob. 117RQCh. 7 - Prob. 118RQCh. 7 - Prob. 119RQCh. 7 - Prob. 120RQCh. 7 - Prob. 121RQCh. 7 - Prob. 122RQCh. 7 - Prob. 123RQCh. 7 - Prob. 124RQCh. 7 - Prob. 125RQCh. 7 - Prob. 127RQCh. 7 - The drinking water needs of a production facility...Ch. 7 - Prob. 129RQCh. 7 - Prob. 131RQCh. 7 - Prob. 132RQCh. 7 - Prob. 133RQCh. 7 - Prob. 134RQCh. 7 - Prob. 136RQCh. 7 - Prob. 137RQ
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