FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
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Chapter 9, Problem 82P
Consider the steady, two-dimensional, incompressible velocity field,
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4 = 3x2 – y represents a stream function in a two – dimensional flow. The
velocity component in 'x' direction at the point (1, 3) is:
1. For incompressible flows, their velocity field
2. In the case of axisymmetric 2D incompressible flows,
where is Stokes' stream function, and
u = VXS,
S(r, z, t) =
Uz =
where {r, y, z} are the cylindrical coordinates in which the flow is independent on the coordinate and hence
1 Ꭷ
r dr
1 dy
r dz
Show that in spherical coordinates {R, 0, 0} with the same z axis, this result reads
Y(R, 0, t)
R sin 0
S(R, 0, t)
UR
uo
Y(r, z, t)
r
=
=
-eq,
and
Up = =
1
ay
R2 sin Ꮎ ᎧᎾ
1 ƏY
R sin Ꮎ ᎧR
-eq
2
(1)
(2)
(3)
Two velocity components of a steady, incompressible flow field are known: u = 2ax + bxy + cy2 and ? = axz − byz2, where a, b, and c are constants. Velocity component w is missing. Generate an expression for w as a function of x, y, and z.
Chapter 9 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
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