A Newtonian fluid flows in an annular space created by a concentric pipe of radius R. and a rod of radius R, as shown in Figure Q1(b). The rod is moving at a constant velocity V, while the pipe is stationary. The flow is steady, laminar and incompressible and there is no forced pressure gradient driving the flow. Assuming the velocity components in the radial and tangential directions are zero and ignoring the effects of gravity, derive an expression for the velocity field in the annular space.

I am confused whether points A and B do not lie on the same streamline in this equation.

A Newtonian fluid is flowing in the narrow gap between two infinite parallel horizontal plates due to the movement of the top plate (see the figure below). The top plate is moving at a speed U from left to right, and the bottom plate is stationary. Consider the flow is steady, incompressible, and laminar. The distance between two plate is H, and the gravity acts in negative z-direction (which is perpendicular into the page). There is an applied constant pressure gradient of apJəx in the x-direction. Calculate the velocity and pressure fields. Plot typical velocity profiles in dimensionless form for a pressure gradient value of 0 and -15. In your solution show the conceptual diagram of the problem; write all relevant assumptions and boundary conditions; show the detailed steps of the problem solutions including equations and detailed processing of those equations. Moving plate Fluid: p.H Fixed plate P2-P1

In plane stagnation flow, an incompressible fluid occupying the space y>0 has one velocity component given by Vx-x. The flow is two-dimensional and steady, such that V₂=0 and nothing depends on z or time t. (a) Use the continuity equation to determine Vy(x,y), given that Vy(x,0) =0. (This condition for Vy corresponds to the plane y=0 being an impenetrable boundary.) (b) is arbitrary, so you may set Y=0 at any convenient location.) Determine the stream function for this flow, (x,y). (The absolute value of