Fox and McDonald's Introduction to Fluid Mechanics
Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Chapter 9, Problem 1P

The roof of a minivan is approximated as a horizontal flat plate. Plot the length of the laminar boundary layer as a function of minivan speed, V, as the minivan accelerates from 10 mph to 90 mph.

Expert Solution & Answer
Check Mark
To determine

The plot of the length of the laminar boundary versus minivan speed.

Explanation of Solution

Given:

The initial speed of the minivan (V1) is 10mph.

The final speed of the minivan (V2) is 20mph.

Calculation:

The Reynolds number for the laminar boundary layer is 5×105.

Refer the appendix, Table A.9 “Properties of Air at Atmospheric Pressure (U.S. Customary Units)” for the temperature of 68°F.

  μ=3.379×107 lbfs/ft2×5ρ=0.00234 slugs/ft3

Calculate the expression for the length of the laminar boundary layer using the Reynolds number (Re).

  Re=ρVLμL=ReμρV

Substitute the known values in the above Equation.

  L=3.379×107 lbfs/ft2×5×1050.00234 slugs/ft3×V=80.342V        (I)

Use the spread sheet and equation (I), calculate the length of minivan for various speed range from 10 to 90 mph.

V1(mph)V1(ft/s)L(ft)
1014.66675.477851
2029.33342.738926
3044.00011.82595
4058.66681.369463
5073.33351.09557
6088.00020.912975
70102.66690.78255
80117.33360.684731
90132.00030.60865

Use the above table values; plot the length of the laminar boundary layer as a function of minivan speed as shown in the figure below:

Fox and McDonald's Introduction to Fluid Mechanics, Chapter 9, Problem 1P

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Chapter 9 Solutions

Fox and McDonald's Introduction to Fluid Mechanics

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