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.