Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 10, Problem 92P
To determine
The apparent thickness of the plate at downstream.
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Students have asked these similar questions
A flat plate of length equal to 50 cm is parallel to a 25 m/s stream velocity. What is the shear stress, in Pa, at a section
40 cm away from the leading edge of the plate? The fluid is air with density equal to 1.2 kg/m³ and kinematic viscosity
of 1.5 x 10-5 m²/s.
Answer:
An approximation for the boundary-layer shape in
is the formula
u(y) - U sin
0 sys d
where U is the stream velocity far from the wall and d is the
boundary layer thickness, as in Fig.
If the fluid is
helium at 20°C and 1 atm, and if U = 10.8 m/s and 8= 3 cm,
use the formula to (a) estimate the wall shear stress Tw in
Pa, and (b) find the position in the boundary layer where t
is one-half of Tw.
-- y = 6
u(y)
2.0 m
7:
10.0 m
= 2²-²²
Us
B
10.0 m
Figure Q1-2
Question 2
Air flow at a constant speed (Us = 10 m/s) is forming a two-dimensional incompressible
laminar boundary layer along a flat plate The velocity profile inside the boundary layer is
given by:
2.0 m
(Equation 1)
At x = 1.00 m, the boundary layer thickness is given as 6.6094 mm. At this location:
a) Determine the shear stress at the wall, at y = 3 mm and y = 10 mm.
b) Calculate the boundary layer displacement thickness.
c) Calculate the mass flow rate through the boundary layer per unit width.
d) Calculate the mass flow rate per unit width of an ideal flow going through the same
height as the boundary layer thickness.
e) Through calculation relate the difference between the mass flow rates in parts (c)
and (d) to the local boundary layer displacement thickness. In not more than 60
word justify your answer. Use sketch(s) to illustrate your justification.
f) Does the assumed velocity profile satisfy the pressure boundary condition? In…
Chapter 10 Solutions
Fluid Mechanics: Fundamentals and Applications
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