Example 6:
A flat plate of length ℓ = 0.500 m and width b = 3.00 m is immersed in a fluid stream
with velocity U = 1.00 m/s that is aligned with ℓ . Find the drag on one side of the plate
and disturbance thickness at the end of the plate for (a) air and (b) water at STP. (c)
Assuming laminar flow, how do the drag and disturbance thickness change if the plate
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is rotated 90˚?
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Known: External flow over a flat plate, ℓ = 0.500 m, b = 3.00 m, U = 1.00 m/s, air/water
Assumptions: Steady,File:U:\EES_Files\ME_347\Examples\Example_6.EES
incompressible, Newtonian fluid, uniform external velocity field 1/25/2016 8:45:56 AM
EES Ver. 9.925: #0552: for use only by students and faculty, Mechanical Engineering, Dept. Cal Poly State University
parallel to plate, negligible end
effects (2-dimensional boundary layer flow), smooth
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edges and plate, transition from laminar to turbulent flow at Rexcr = 5 x 105
Find: FD and δ for (a) air and (b) water
10
Solution:
water
Friction Drag (N)
1
L = 0.500 m
b = 3.00 m
0.1
Properties: at standard temperature (15 ˚C) and pressure (1 atm)
Air:
Water:
3
ρ = 1.23 kg/m
ρ = 1000 kg/m3
0.01
-5
air
2
ν = 1.46 x 10 m /s
-6
ν = 1.02 x 100.001
m2/s
Files\ME_347\Examples\Example_6.EES
1/25/2016
8:45:56 AM Page 3
0.0001
Answers:
(a) 0.00662
13.5 Engineering,
mm, (b) Dept.
1.42CalN,Poly
3.57
0.0 mm
0.5
S Ver. 9.925: #0552: for
use only by students
and faculty, N,
Mechanical
State
University
1.0
1.5
2.0
Freestream Velocity (m/s)
10
water
Disturbance Thickness (mm)
1
50
Friction Drag (N)
L = 0.500 m
b = 3.00 m
0.1
air
0.01
0.001
0.0001
0.0
0.5
1.0
1.5
2.0
b = 3.00 m
30
20
air
10
0
0.0
water
0.5
1.0
1.5
2.0
Freestream Velocity (m/s)
Freestream Velocity (m/s)
Disturbance Thickness (mm)
L = 0.500 m
40
Figure
1. Friction drag and disturbance thickness at the end of a flat plate aligned
50
with the flow that is 0.500 m long and 3.00 m wide as a function of
L = 0.500
m
free stream
velocity
for air and water at STP.
40
b = 3.00 m
30
20
air
10
0
0.0
water
0.5
1.0
1.5
Freestream Velocity (m/s)
2.0