Derive the equation for the exact fluid velocities

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Reference no: EM131500613

Question: The leakage flow of hydraulic fluid through the gap between a piston-cylinder arrangement may be modeled as laminar flow of fluid between infinite parallel plates, as shown in the ac-companying figure. This model offers reasonable results for relatively small gaps The differential equation governing the flow is

Where µ is the dynamic viscosity of the hydraulic fluid, u is the fluid velocity, and is the pressure drop and is constant. Derive the equation for the exact fluid velocities Assume an approximate fluid velocity solution of the form . Use the following methods to evaluate

(a) the collocation method and

(b) the subdomain method. Corn-pare the approximate results to the exact solution.

Reference no: EM131500613

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