H5.1 A cylindrical tank of diameter D has a conical contraction and an exit hole of...

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H5.1 A cylindrical tank of diameter D has a conical contraction and an exit hole of diameter d at the tank bottom. The fluid level in the tank is h. The velocity of the fluid leaving the tank is V. Assume incompressible flow with fluid density, p. a. Derive an expression for the rate of change of the water level, dh/dt, in terms of known quantities and assuming V is constant. b. Consider a D = 20 cm tank of water with d = 3 cm exit and V 3.2 m/s. Integrate the result in part a. and determine the time [s] it takes for the water level to drop from an initial value, h = 50 cm, to a value, h = 20 cm. = D- h(t) d V Fig. H5.1 H5.1 A cylindrical tank of diameter D has a conical contraction and an exit hole of diameter d at the tank bottom. The fluid level in the tank is h. The velocity of the fluid leaving the tank is V. Assume incompressible flow with fluid density, p. a. Derive an expression for the rate of change of the water level, dh/dt, in terms of known quantities and assuming V is constant. b. Consider a D = 20 cm tank of water with d = 3 cm exit and V 3.2 m/s. Integrate the result in part a. and determine the time [s] it takes for the water level to drop from an initial value, h = 50 cm, to a value, h = 20 cm. = D- h(t) d V Fig. H5.1