Consider a potential flow describing a uniform flow around a rotating cylinder. It is rotating such that there are two stagnation points that are 90° apart. Write an expression for the pressure on the surface of the cylinder as a function of 0? Your answer should be in terms of the upstream velocity Uo, upstream pressure po, and fluid density p? Note that your answer should not have either I or the cylinder radius a.

The streamlines in a particular two-dimensional flow field are all concentric circles, as shown in Fig. 5 the equation v, = wr where w is the angular velocity of the rotating mass of fluid. Determine the circulation around the path ABCD. The velocity is given by B Figure 5

An incompressible fluid flows past an impermeable flat plate, as in Fig. . , with a uniform inlet profile u = U, and a cubic polynomial exit profile (3η - η' where n= 2 Compute the volume flow Q across the top surface of the control volume. Ug у 3б Q? Uo y=0 CV Cubic Solid plate, width b into paper

By using the expression for the shear stress derived in class (and in BSL), show that the shear force on asphere spinning at a constant angular velocity in a Stokes’ flow, is zero.This means that a neutrally buoyant sphere (weight equal buoyancy force) that is made to spin in aStokes’ flow, will neither rise nor fall, nor translate in any preferential direction in the (x-y) plane. expressions for velocity are: v_r (r,θ)= U_∞ [1-3R/2r+R^3/(2r^3 )] cos⁡θ v_θ (r,θ)= -U_∞ [1-3R/4r-R^3/(4r^3 )] sin⁡θ Where v_r and v_θ are the radial and angle velocity, U_∞ is the velocity of fluid coming to sphere which very faar away from the sphere. And R is the radius of sphere.

Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.