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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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.
A two-dimensional flow field has an x-component of velocity given in Cartesian coordinates by u = 2x − 3y. (a) Find v, the y-component of velocity, if the flow is incompressible and v = 0 when x = 0. (b) If the flow follows the Bernoulli equation, find an expression for the pressure distribution as a function of x and y, given that the pressure is p0 at the stagnation point.
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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