6-3. Velocity, Vorticity, and Pressure Suppose that for a steady, two-dimensional flow in the region x ≥ 0 and y ≥0, one velocity component is given by where C and m are constants. Vx(x, y) =Cxm (a) Assuming that the fluid is incompressible and that vy(x, 0) = 0, determine vy(x,y). (b) For what values of m will the flow be irrotational? (c) For what values of m will the Navier-Stokes equation be satisfied? Determine P(x, y) for those cases, assuming that P(0,0) = P0.

Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Question
6-3. Velocity, Vorticity, and Pressure
Suppose that for a steady, two-dimensional flow in the region x ≥ 0 and y ≥0, one velocity
component is given by
where C and m are constants.
Vx(x, y) =Cxm
(a) Assuming that the fluid is incompressible and that vy(x, 0) = 0, determine vy(x,y).
(b) For what values of m will the flow be irrotational?
(c) For what values of m will the Navier-Stokes equation be satisfied? Determine P(x, y) for
those cases, assuming that P(0,0) = P0.
Transcribed Image Text:6-3. Velocity, Vorticity, and Pressure Suppose that for a steady, two-dimensional flow in the region x ≥ 0 and y ≥0, one velocity component is given by where C and m are constants. Vx(x, y) =Cxm (a) Assuming that the fluid is incompressible and that vy(x, 0) = 0, determine vy(x,y). (b) For what values of m will the flow be irrotational? (c) For what values of m will the Navier-Stokes equation be satisfied? Determine P(x, y) for those cases, assuming that P(0,0) = P0.
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