Fluid mechanics: a water tank is a cylinder 4 m in height and 2 meters in diameter. the tank is full at time to. the tank sits on a platform 12 m tall. a water tap is located at the bottom center of the tank. the tap, when actuated, opens to a pipe 5 cm in radius.
a. write down bernoulli’s equation. identify the pressure, kinetic and potential energy terms. show that each has the units of an energy density (joules/volume).
b. use bernoulli’s equation to compare the difference in pressure between the surface of the water and the bottom of the tank near the edge? assume the fluid is motionless near the edge.
c. when a tap is opened water rushes in to a pipe 5 cm in radius. the pipe is straight and drops 12 m to ground level, but along the way slowly in radius to 2 cm. what is the speed of the water as it emerges from the pipe?
d. use the continuity equation to find the speed of the water as it enters the pipe 12 m above, i. e. bottom of the tank.
e. what is the volume and mass flow rate of the stream of water?
f. what is the pressure of the fluid as it enters the pipe, again at the bottom of the tank.