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 15, Problem 98RQ
To determine

The money wasted per year.

Expert Solution & Answer
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Explanation of Solution

Given:

The diameter of the ball is, D=2.62 in.

The equivalent roughness factor is, ε/D=1.5×103.

Distance travelled per year is, L=16000 miles.

Average speed of the car is, V=55 mph.

The overall efficiency is, η=0.308.

The density of the fuel is, ρfuel=50.2lbm/ft3.

The heating value of the fuel is, HV=1.47×107ftlbf/lbm.

Cost of the fuel is $4.00/gal.

Calculation:

Obtain the following properties of air:

  Density,ρair=0.07518lbm/ft3Viscosity,μair=1.227×105lbm/fts

The Reynolds number is,

  Re=ρairVDμair=(0.07518lbm/ft3)(55×1.466ft/s)(2.62/12 ft)1.227×105lbm/fts=107900

The drag coefficient for a sphere for the above Reynolds number is CD=0.505.

The drag force is,

  FD=CDAρairV22=CD(π4D2)ρairV22

The power required to overcome the resistances is,

  W˙drag=FDL=CD(π4D2)ρairV2L2

The energy provided by the fuel is,

  Ereq=W˙dragη=CD(π4D2)ρairV2L2η

The quantity of fuel required is,

  Vfuel=Ereq/HVρfuel=CD(π4D2)ρairV2L2η(HV)ρfuel=(0.505)[π4(2.62/12 ft)2][(0.07518lbm/ft3)×(55×1.466ft/s)2×(16000×5280ft)2]0.308(1.47×107ftlbf/lbm)(50.2lbm/ft3)=0.05343 ft3×7.481 gal1 ft3=0.3997 gal

The extra cost of fuel is,

  Additional Cost=Vfuel×Cost=(0.3997 gal)($4.00/gal)=$1.6

Thus, the money wasted per year is $1.6.

Since the additional cost is minimal, Jamie need not remove the tennis ball.

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Chapter 15 Solutions

Fundamentals of Thermal-Fluid Sciences

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