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
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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.
Transcribed Image Text: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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