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U2 v(x) A(x) A2 A1

U2 v(x) A(x) A2 A1

Elements Of Electromagnetics
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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U2 v(r) A(x) A2 A1 Figure 2: Control Volume for (a) (a) A nozzle with exit area A, is mounted at the end of a pipe of area A1, as shown in figure 2. The nozzle converges gradually, and we assume that the flow in it is steady, uniform over any particular cross-section x, incompressible, and inviscid. Gravitational effects are, furthermore, taken as negligible. Denote the exit velocity U2 and let the exit pressure p2 equal the atmospheric pressure patm- (i) Show that the volume flow rate in the nozzle given by Q = v(x)A(x) is constant. (ii) Derive an expression for the gauge pressure p,(x) = p(x) – Patm, in terms of Q, p, A2 and A(x).
Transcribed Image Text:U2 v(r) A(x) A2 A1 Figure 2: Control Volume for (a) (a) A nozzle with exit area A, is mounted at the end of a pipe of area A1, as shown in figure 2. The nozzle converges gradually, and we assume that the flow in it is steady, uniform over any particular cross-section x, incompressible, and inviscid. Gravitational effects are, furthermore, taken as negligible. Denote the exit velocity U2 and let the exit pressure p2 equal the atmospheric pressure patm- (i) Show that the volume flow rate in the nozzle given by Q = v(x)A(x) is constant. (ii) Derive an expression for the gauge pressure p,(x) = p(x) – Patm, in terms of Q, p, A2 and A(x).
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