U2v(r)A(x)A2A1Figure 2: Control Volume for (a)(a) A nozzle with exit area A, is mounted at the end of a pipe of area A1, asshown in figure 2. The nozzle converges gradually, and we assume that theflow in it is steady, uniform over any particular cross-section x,incompressible, and inviscid. Gravitational effects are, furthermore, takenas negligible. Denote the exit velocity U2 and let the exit pressure p2 equalthe atmospheric pressure patm-(i) Show that the volume flow rate in the nozzle given by Q = v(x)A(x) isconstant.(ii) Derive an expression for the gauge pressure p,(x) = p(x) – Patm, interms of Q, p, A2 and A(x).

Givenincompressible fluid flowing through nozzleArea of the pipe =A1velocity in the pipe=U1nozzle…

Answered: U2 v(x) A(x) A2 A1

Engineering

Mechanical Engineering

U2 v(x) A(x) A2 A1

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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Question

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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