(a) Extend the control volume analysis used to derive the continuity equation to three-dimensional unsteady flows and show that Eq. (2.2a) can be written as ap a a + (pu) + (pv) + (pw) - 0. ay (P2.1) at a az (b) Deduce from Eq. (P2.1) the mass conservation equations for three-dimen- sional steady or unsteady constant-density flow and for three-dimensional steady, variable-density flows corresponding to Eqs. (2.2b) and (2.2c) for two-dimensional flows. c) Show that Eq. (P2.1) can be rewritten as a transport equation for p, using the three-dimensional version of the d/dt operator defined in Eq. (2.10).

(a) Extend the control volume analysis used to derive the continuity equation to three-dimensional unsteady flows and show that Eq. (2.2a) can be written as ap a a + (pu) + (pv) + (pw) - 0. ay (P2.1) at a az (b) Deduce from Eq. (P2.1) the mass conservation equations for three-dimen- sional steady or unsteady constant-density flow and for three-dimensional steady, variable-density flows corresponding to Eqs. (2.2b) and (2.2c) for two-dimensional flows. c) Show that Eq. (P2.1) can be rewritten as a transport equation for p, using the three-dimensional version of the d/dt operator defined in Eq. (2.10).

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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