Oil μ=0.4N * s/m2 flows between two fixed horizonta; infinite parallel plates with a spacing of 5mm. the flow is laminar and steady with a pressure gradient of -900 N/m2
Determine the volume flow rate per unit width and the shear stress of the upper plate (Start with the full, three-dimensional Navier-Stokes equations and the continuity equation, simplify them, and then solve them for the given situation. Do not just use the equations developed in the text – you must show how these equations were developed.
Hint: For the boundary conditions for this flow, use that the velocity gradient,∂u/∂y= 0, in the centre of the flow and the no-slip condition on the pipe wall. Also, carry through ∂p*/∂x as a constant through your integration.