With reference to a standard Cartesian (x, y) plane, the parabolic velocity distribution profile of fully developed laminar flow in x direction between two parallel stationary and identical plates that are separated by distance, h is given by the expression

Consider the flow of water through a clear tube. It is sometimes possible to observe cavitation in the throat created by pinching off the tube to a very small diameter as sketched. We assume incompressible flow with negligible gravitational effects and negligible irreversibilities. You will learn that as the duct cross- sectional area decreases, the velocity increases and the pressure decreases according to    V1A1 = V2 A2 and P1 + ρ V21 / 2 = P2 + ρ V2 2 / 2respectively, where V1 and V2 are the average velocities through cross-sectional areas A1 and A2. Thus, both the maximum velocity and minimum pressure occur at the throat. (a) If the water is at 20°C, the inlet pressure is 20.803 kPa, and the throat diameter is one-twentieth of the inlet diameter, estimate the minimum average inlet velocity at which cavitation is likely to occur in the throat. (b) Repeat at a water temperature of 50°C. Explain why the required inlet velocity is higher or lower than that of part (a).