Fox And Mcdonald's Introduction To Fluid Mechanics
9th Edition
ISBN: 9781118921876
Author: Pritchard, Philip J.; Leylegian, John C.; Bhaskaran, Rajesh
Publisher: WILEY
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Textbook Question
Chapter 5, Problem 50P
Determine the velocity potential for
- (a) a flow field characterized by the stream function ψ = 3x2y − y3.
- (b) a flow field characterized by the stream function ψ = xy.
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(a) A two-dimensional flow field is given byu = 5x 2 − 5y 2v = −10xy(i) Find the streamfunction ψ and velocity potential φ.(ii) Find the equation for the streamline and potential line which passesthrough the point (1, 1).
velocity field is given by:
A two-dimensional
V = (x - 2y) i- (2x + y)Ĵj
a. Show that the flow is incompressible and irrotational.
b. Derive the expression for the velocity potential, (x,y).
c. Derive the expression for the stream function, 4(x,y).
The velocity components in the x and y
directions are given by
3
u = Axy3 - x2y, v = xy2 --
The value of a for a possible flow field
involving an incompressible fluid is
Chapter 5 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
Ch. 5 - Which of the following sets of equations represent...Ch. 5 - Which of the following sets of equations represent...Ch. 5 - In an incompressible three-dimensional flow field,...Ch. 5 - In a two-dimensional incompressible flow field,...Ch. 5 - The three components of velocity in a velocity...Ch. 5 - The x component of velocity in a steady,...Ch. 5 - The y component of velocity in a steady...Ch. 5 - The velocity components for an incompressible...Ch. 5 - The radial component of velocity in an...Ch. 5 - A crude approximation for the x component of...
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- 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.arrow_forwardThe stream function of a flow field is y = Ax3 – Bxy², where A = 1 m1s1 and B = 3 m-1s1. (a) Derive the velocity vector (b) Prove that the flow is irrotational (c) Derive the velocity potentialarrow_forwardThe stream function o in a two-dimensional flow field is given as 9 = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. Find the potential flow function P(x, y) for this flow field with boundary condition 0 = 0 at x = 2, y = 1. (b)arrow_forward
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