Q4) An incompressible, viscous fluid is placed between horizontal, infinite, parallel plates as is shown in Fig.. The two plates move in opposite directions with constant velocities, and as shown. The pressure gradient in the x direction is zero, and the only body force is due to the fluid weight. Use the Navier-Stokes equations to derive an expression for the velocity distribution between the plates. Assume laminar flow. →UI b 12 L₂x 50₂

The block slides at a constant speed on a surface with friction. In each case, the water jet has velocity 50 m/s and cross-sectional area 5 cm2, and the block has velocity 25 m/s. In case (a), the jet is deflected to an angle of 60° from horizontal relative to the block, as shown. In case (b), the jet is deflected 180°. Calculate the friction force in each case. Apply both a moving Reference Frame (RF) and a fixed RF. Use the VSM. Check that both RFs give the same friction force for a given case. (We would not expect the two cases to have the same friction force!) Density of water is 1000 kg/m3. All jets are open to the atmosphere. case (a) 60° case (b)

a,b please

Consider the two-dimensional flow of an inviscid, incompressible fluid described by the superposition of a parallel flow of velocity V0, a source of strength q, and a sink of strength −q, separated by a distance b in the direction of the parallel flow, the source being upstream of the sink. (a) Find the resultant stream function and velocity potential. (b) Sketch the streamline pattern. (c) Find the location of the upstream stagnation point relative to the source.