The two-dimensional incompressible flow-field around a Rankine vortex of strength r and core size R, has only a circumferential component, v. The value of v is given as follows: R г Tr v(r) r R v(r) 2r Determine the vorticity of this flow-field and the pressure coefficient, Cp, and plot them as a function of r/R. The non-dimensional pressure coefficient C, is defined below. Where is the pressure expected to be minimum, and what is the value of the minimum C,? (Use polar coordinates) p – P C, where pe is the pressure at infinity, and p is the density of the fluid. Vr is the flow velocity at the outer edge of the vortex core (i.e. at r = R)
The two-dimensional incompressible flow-field around a Rankine vortex of strength r and core size R, has only a circumferential component, v. The value of v is given as follows: R г Tr v(r) r R v(r) 2r Determine the vorticity of this flow-field and the pressure coefficient, Cp, and plot them as a function of r/R. The non-dimensional pressure coefficient C, is defined below. Where is the pressure expected to be minimum, and what is the value of the minimum C,? (Use polar coordinates) p – P C, where pe is the pressure at infinity, and p is the density of the fluid. Vr is the flow velocity at the outer edge of the vortex core (i.e. at r = R)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:The two-dimensional incompressible flow-field around a Rankine vortex of strength r and core size R,
has only a circumferential component, v. The value of v is given as follows:
R
г
v(r)
Tr
r< R
27 R?
v(r)
r > R
2r
Determine the vorticity of this flow-field and the pressure coefficient, Cp, and plot them as a function of
r/R. The non-dimensional pressure coefficient C, is defined below. Where is the pressure expected to
be minimum, and what is the value of the minimum C,? (Use polar coordinates)
p - Poo
Cp
where p. is the pressure at infinity, and p is the density of the fluid. VR is the flow velocity at the outer
edge of the vortex core (i.e. at r= R)
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