Q5 95 Marks-50 (a) With suitable diagram, derive the pressure differential equation for a fluid body. Hence, deduce the expression of piezometric head for fluid at rest. (b) With necessary assumptions, derive Bernoulli's equation for steady, incompressible flow. Hence, explaining each term, show that Bernoulli equation is the conservation of energy for an inviscid fluid system. (c) With suitable schematic diagram and assumptions, derive the expression of actual flow rate of an orifice meter for an inclined pipe. Define the coefficient of discharge, velocity, and contraction. (d) Deduce the expression of velocity profile for fully developed laminar flow in a circular pipe, and then prove that, the average velocity of flow is 1/2 (one-half) of the maximum velocity.