H dy² dp da Th DI constant da (4) u(y) = A [sin (T) H (3) [2] 165 041 = Figure.1: Laminar flow of fluid between infinite parallel plates where u is the dynamic viscosity of the hydraulic fluid, u is the fluid velocity, and dP/dx is the pressure drop and is constant. Derive the equation for the exact fluid velocities. Assume an approximate fluid velocity solution of the form:

H dy² dp da Th DI constant da (4) u(y) = A [sin (T) H (3) [2] 165 041 = Figure.1: Laminar flow of fluid between infinite parallel plates where u is the dynamic viscosity of the hydraulic fluid, u is the fluid velocity, and dP/dx is the pressure drop and is constant. Derive the equation for the exact fluid velocities. Assume an approximate fluid velocity solution of the form:

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 Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

I want to answer all the questions by handwriting.

The leakage flow of hydraulic fluid through the gap between a piston-cylinder arrangement may
be modelled as laminar flow of fluid between infinite parallel plates, as shown in Figure.1
. The problem is a practical example of the applications of FEA approach and this model offers
reasonable results for relatively small gaps. The differential equation governing the flow is:
H
dp
dr
d²u
dy²
Th
d.P
dx
constant
145-10
u(y) = A [sin (77)]
H
edg
0
Figure.1: Laminar flow of fluid between infinite parallel plates
where u is the dynamic viscosity of the hydraulic fluid, u is the fluid velocity, and dP/dx is the
pressure drop and is constant. Derive the equation for the exact fluid velocities. Assume an
approximate fluid velocity solution of the form:
Note that the domain is divided into 4 elements with equal lengths, use the following methods to
evaluate U2,U3, U4: a) the collocation method, (b) the subdomain method (c) the Galerkin method (d)
One Dimensional FEM based on Galerkin method(element matrices-Galerkin method). Compare the
approximate results to the exact solution at the nodes if µ-0.02 N.s/m², dp/dx= -1x108pa/m and
H=1x105 m.

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