(a) Use the y-momentum equation to show that the pressure gradient across the boundary layer is approximately zero i.e. - 0. Assume the boundary layer to be a two-dimensional ду steady and incompressible flow. Neglect gravitational forces. State clearly all assumptions made. Use the Bernoulli's equation to prove that the pressure difference is given by (b) P2-P1 = -4pU? for a fluid with constant density p flowing from point 1 to point 2 where pi, Ui, A1 are the pressure, velocity and flow cross-section area at point 1 and p2, U2, A2 are the pressure, velocity and flow cross-section area at point 2 respectively. A1 A2 The ratio of the cross-section area = 3.

(a) Use the y-momentum equation to show that the pressure gradient across the boundary layer is approximately zero i.e. - 0. Assume the boundary layer to be a two-dimensional ду steady and incompressible flow. Neglect gravitational forces. State clearly all assumptions made. Use the Bernoulli's equation to prove that the pressure difference is given by (b) P2-P1 = -4pU? for a fluid with constant density p flowing from point 1 to point 2 where pi, Ui, A1 are the pressure, velocity and flow cross-section area at point 1 and p2, U2, A2 are the pressure, velocity and flow cross-section area at point 2 respectively. A1 A2 The ratio of the cross-section area = 3.

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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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

(a)
Use the y-momentum equation to show that the pressure
gradient across the boundary layer is approximately zero i.e.
= 0 . Assume the boundary layer to be a two-dimensional
ду
steady and incompressible flow. Neglect gravitational
forces. State clearly all assumptions made.
Use the Bernoulli's equation to prove that the pressure
difference is given by
(b)
P2-P1 = -4pU?
for a fluid with constant density p flowing from point 1 to
point 2 where pi, U1, A1 are the pressure, velocity and flow
cross-section area at point 1 and p2, U2, A2 are the pressure,
velocity and flow cross-section area at point 2 respectively.
The ratio of the cross-section area
A1
= 3.

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