FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
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Chapter 9, Problem 104P
To determine
The mathematical equation for each boundary condition.
The pressure boundary condition is appropriate for this flow field.
The velocity boundary conditions in terms of cylindrical coordinates and velocity component at free surface.
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Consider liquid in a cylindrical tank. Both the tank and the liquid rotate as a rigid
body. The free surface of the liquid is exposed to room air. Surface tension effects
are negligible. Present the boundary conditions required to solve this problem.
Specifically, what are the velocity boundary conditions in terms of cylindrical
coordinates (r, 0, z) and velocity components (ur, uo, U:) at all surfaces, including the
tank walls and the free surface? What pressure boundary conditions are appropriate
for this flow field? Explain.
Free
surface
Ps Paa
Liquid
Please help me to answer number (a) with detailed explanation by today. thank you
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 9 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
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