Chapter 15
Flow Over Bodies: Drag and Lift
Flow over Flat Plates
1543C
The fluid viscosity is responsible for the development of the velocity boundary layer. For the
idealized inviscid
fluids (fluids with zero viscosity), there will be no velocity boundary layer.
1544C
The friction coefficient represents the resistance to fluid flow over a flat plate. It is proportional to
the drag force acting on the plate. The drag coefficient
for a flat surface is equivalent to the mean friction
coefficient.
1545C
The friction coefficient will change with position in laminar flow over a flat plate (it will decrease
along the plate in the flow direction).
1546C
The average friction coefficient in flow over a flat plate is determined by integrating the local
friction coefficient over the entire plate, and then dividing it by the length of the plate. Or, it can be
determined experimentally by measuring the drag force, and dividing it by the dynamic pressure.
1547E
Light oil flows over a flat plate. The total drag force per unit width of the plate is to be determined.
Assumptions
1
The flow is steady and incompressible.
2
The critical Reynolds number is Re
cr
= 5 × 10
5
.
3
The surface of the plate is smooth.
Properties
The density and kinematic viscosity of light oil at 75°F are
= 55.3 lbm/ft
3
and
= 7.751×10
–3
ft
2
/s (Table A19E).
Analysis
Noting that
L
= 15 ft, the Reynolds number at the end of the plate is
4
2
3
10
161
.
1
/s
ft
10
751
.
7
ft)
ft/s)(15
6
(
Re
L
L
V
which is less than the critical Reynolds number. Thus we have
laminar flow
over the entire plate, and the average friction coefficient is determined from
01232
.
0
)
10
161
.
1
(
328
.
1
Re
328
.
1
5
.
0
4
5
.
0
L
f
C
Noting that the pressure drag is zero and thus
f
D
C
C
for a flat plate, the
drag force acting on the top surface of the plate per unit width becomes
lbf
5.87
2
2
3
2
2
ft/s
lbm
32.2
lbf
1
2
ft/s)
6
)(
lbm/ft
8
.
56
(
)
ft
1
15
(
01232
.
0
2
V
A
C
F
f
D
The total drag force acting on the entire plate can be determined by multiplying the value obtained above
by the width of the plate.
Discussion
The force per unit width corresponds to the weight of a mass of 5.87 lbm. Therefore, a person
who applies an equal and opposite force to the plate to keep it from moving will feel like he or she is using
as much force as is necessary to hold a 5.87 lbm mass from dropping.
1522
6 ft/s
Oil
L
= 15 ft
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Chapter 15
Flow Over Bodies: Drag and Lift
1548
Air flows over a plane surface at high elevation. The drag force acting on the top surface of the plate
is to be determined for flow along the two sides of the plate.
Assumptions
1
The flow is steady and incompressible.
2
The critical Reynolds number is Re
cr
= 5
10
5
.
3
Air is an ideal gas.
4
The surface of the plate is smooth.
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 Spring '08
 Chung
 Fluid Dynamics, Drag force

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