Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Chapter 2, Problem 6P
When an incompressible, nonviscous fluid flows against a plate in a plane (two-dimensional) flow, an exact solution for the equations of motion for this flow is u = Ax, υ = −Ay, with A > 0 for the sketch shown. The coordinate origin is located at the stagnation point 0, where the flow divides and the local velocity is zero. Plot the streamlines in the flow.
P2.6
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3.7. In Fig. 3.4b is shown the unsteady-state streamlines of a cylinder moving
with a uniform velocity U in the fluid at rest. Calculate and draw the un-
steady-state streamlines at an interval of 10° (0 = 10°). The tangential com-
ponent of velocity on the surface of the cylinder in a uniform stream, U.,
is given by r = -2U sin 0.
2. Consider a stream function given by = (²+x²).
(a) Does this flow satisfy conservation of mass? Show your work.
(b) Plot the streamlines for this flow. Let K= 2. Be sure to indicate the direction of the flow.
(c) Is this flow irrotational? If so, find the velocity potential for this flow. If not, show that a
velocity potential does not exist.
(d) Describe the flow represented by this stream function.
The velocity components of a flow field are given by:
= 2x² – xy + z²,
v = x² – 4xy + y²,
w = 2xy – yz + y²
(i) Prove that it is a case of possible steady incompressible fluid flow
(ii) Calculate the velocity and acceleration at the point (2,1,3)
Chapter 2 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
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