FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
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Chapter 4, Problem 40P
A steady, incompressible, two-dimensional velocity fie is given by
where the x-and y-coordinates and m the magnitude of velocity is in m/s.
(a) Determine if there are any stagnation points in this field and if so where they are.
(b) Sketch velocity vectors at several locations in the upper-right quadrant for x= 0 m to 4 in and y = 0 in to 4 m; qualitatively describe the flow field.
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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)
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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)
In plane stagnation flow, an incompressible fluid occupying the space y>0 has one
velocity component given by Vx-x. The flow is two-dimensional and steady, such that
V₂=0 and nothing depends on z or time t.
(a)
Use the continuity equation to determine Vy(x,y), given that Vy(x,0) =0.
(This condition for Vy corresponds to the plane y=0 being an impenetrable boundary.)
(b)
is arbitrary, so you may set Y=0 at any convenient location.)
Determine the stream function for this flow, (x,y). (The absolute value of
4. Consider a velocity field V = K(yi + ak) where K is a constant. The vorticity, z , is
(A) -K
(B) K
(C) -K/2
(D) K/2
Chapter 4 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
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