Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 7, Problem 7.93P
A hot-film probe is mounted on a cone-and-rod system in a sea- level airstream of 45 m/s, as in Fig. P7.93. Estimate the maxim um cone vertex angle allowable if the flow-induced bending moment at the root of the rod is not to exceed 3ON. cm.
P7.93
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1. A hydrofoil 0.366 m long and 1.82 m wide is placed in a water flow of 12.9 m/s,
with p = 1025.3 kg/m and v =1.02x 106 m²/s. Estimate the boundary layer
thickness at the end of the plate, and the friction drag from the leading edge.
2. Water flows at a velocity of 1.2 m/s over a flat plate 1.2 m long. Assume 1/7th
power law and determine the boundary layer thickness and displacement
thickness. Compare the values with values calculated using laminar flow
correlations. v = 1 x 10-6m²/s.
3. The velocity components in a two dimensional flow field for an incompressible
fluid are expressed as
3
v= xy? – 2y –,
(a) Show that these functions represents a possible case of an irrotational flow,
(b) obtain an expression for the stream function y and
(c) obtain an expression for the velocity potential o.
4. The flow represented by y = xy, determine
(a) the velocity components
(b) the rotational character
(c) the shearing strain rates a
5. The stream function for a two-dimensional…
Using von Karman momentum integral, derive boundary layer height 8, boundary
layer displacement thickness d, boundary layer momentum thickness 0, wall shear
stress To, local skin friction coefficient c, and total drag coefficient C, for turbulent
boundary layer flow with power law constant, n = 5. Discuss by comparing your
answers to turbulent boundary layer flow with power law constant, n = 7.
Take the empirical wall shear stress:
To = 0.0204pU
2
%3D
SU
1/4
3. Pressure Flow, Flat Plates. Adverse pressure gradients in flow over bodies lead to flow reversal &
separation, wakes, and increased drag. To examine such behavior, consider fully developed, laminar flow
between two flat pates a distance 8 apart. The bottom plate is fixed, and the top plate moves with speed U
(representing the outer flow over a boundary layer of thickness 8). (a) Derive the critical adverse pressure
gradient, (dp/dx)*, above which there will be flow reversal, by solving the N-S equation in the coordinates
shown, to get a relation for u(y), du/dy, and the critical (dp/dx)* in terms of 8, U, and u above which there
μ
will be flow reversal at the lower plate. (b) If 8 = 5 mm and U = 10 m/s, evaluate (dp/dx)* if the fluid is air.
Moving
plate
Fixed
plate
2/
1.0
0.8
0.6
0.4
0.2
Back-
flow
P=-3
0
-0.4 -0.2
0 0.2
0.4
u
U
(b)
U
0.6 0.8 1.0 1.2
b
1.4
(a)
FIGURE 6.30 Viscous flow between parallel plates with the bottom plate fixed and the
upper plate moving (Couette flow): (a)…
Chapter 7 Solutions
Fluid Mechanics
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