Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 4, Problem 4P
Consider the following steady, two-dimensional velocity field:
Is there a stagnation point in this flow field? If so, where is it?
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(b)
Two velocity components of a steady, incompressible flow field are given
as follows;
u = 2ax + bxy + cy?
v = axz – byz?
where a, b and c are constants. Determine an expression for w as a
function of x, y, and z.
The velocity of flow of fluid is represented by the equation: V=2xi +3vj. The equation of the stream line passing through the point (4,3) is (A) 0.72x = 1,2
(B)¹ = 0.72x¹/²
(C) 0.72x2=2
(D) None of these
Consider the following steady, two-dimensional velocity field: V = (u, v) = (0.5 + 1.2x)i + (-2.0 – 1.2y)j. Is there
a stagnation point in this flow field? If so, where is it?
Chapter 4 Solutions
Fluid Mechanics: Fundamentals and Applications
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- 1. A Cartesian velocity field is defined by V = 2xi + 5yz2j − t3k. Find the divergence of the velocity field. Why is this an important quantity in fluid mechanics? 2. Is the flow field V = xi and ρ = x physically realizable? 3. For the flow field given in Cartesian coordinates by u = y2 , v = 2x, w = yt: (a) Is the flow one-, two-, or three-dimensional? (b) What is the x-component of the acceleration following a fluid particle? (c) What is the angle the streamline makes in the x-y plane at the point y = x = 1?arrow_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_forwardTwo 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_forward
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