(1) Basic Concepts Show that a stress and a momentum flux have the same unit by showing that a force and the rate of momentum change or transfer have the same unit. (2) Overall Mass Balance Equation An incompressible fluid is flowing through a circular conduit, as shown in the figure below Fig P1.2-1. The velocity profile of the fluid in the 8-cm-diameter pipe is cm/s What is the average velocity in the 2-cm-diameter pipe? 2cm 8cm Tube (3) Overall Momentum Balance Equation A horizontal turbulent liquid jet of diameter Dand average velocity v, impinges on a vertical plate mounted on a cart, thus exerting a force F on a plate, as shown in Fig. P1.4-3. Determine the opposing force needed to keep the plate moving at a constant velocity v, (< v). Neglect the viscous and gravity forces. (Hint: Let the control volume Q move with the plate) Nozzia Cart 1|Page (4) Differential Momentum Balance Equation Consider the incompressible Newtonian fluid flowing, under the pressure gradient dp/dz, between two stationary horizontal plates separated by a gap of 2L, as shown in the following figure. The volume flow rate (a) Find the steady-state velocity distribution and (b) Find the shear force acting on the two plates by the fluid. O is known. Stationary plate, vz =0 Fluid 2L Stationary plate, Vz =0

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Transcribed Image Text:(1) Basic Concepts Show that a stress and a momentum flux have the same unit by showing that a force and the rate of momentum change or transfer have the same unit. (2) Overall Mass Balance Equation An incompressible fluid is flowing through a circular conduit, as shown in the figure below Fig P1.2-1. The velocity profile of the fluid in the 8-cm-diameter pipe is v, = 0.1 ст/s What is the average velocity in the 2-cm-diameter pipe? 2cm 8cm Tube (3) Overall Momentum Balance Equation Ahorizontal turbulent liquid jet of diameter Dand average velocity v, impinges on a vertical plate mounted on a cart, thus exerting a force F on a plate, as shown in Fig. P1.4-3. Determine the opposing force needed to keep the plate moving at a constant velocity v, (< v). Neglect the viscous and gravity forces. (Hint: Let the control volume Q move with the plate) Plate Nozzle 1|Page (4) Differential Momentum Balance Equation Consider the incompressible Newtonian fluid flowing, under the pressure gradient dp/dz, between two stationary horizontal plates separated by a gap of 2L, as shown in the following figure. The volume flow rate Q is known. (a) Find the steady-state velocity distribution and (b) Find the shear force acting on the two plates by the fluid. Stationary plate, vz =0 AY Fluid 2L Stationary plate, vz =0

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