Fluid Mechanics: A water tank is a cylinder 4 m in height and 2meters in diameter. The tank is full at timeto. The tank sits on a platform 12 m tall. Awater 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’sequation. Identify the Pressure, Kinetic and Potential Energyterms. Show that each has the units of an energy density(Joules/Volume).
b.      Use Bernoulli’s equationto compare the difference in pressure between the surface of thewater and the bottom of the tank near the edge? Assume the fluid ismotionless near the edge.
c.      When a tap is openedwater rushes in to a pipe 5 cm in radius. The pipe is straight anddrops 12 m to ground level, but along the way slowly in radius to 2cm. What is the speed of the water as it emerges from the pipe?
d.      Use the continuityequation to find the speed of the water as it enters the pipe 12 mabove, i.e. bottom of the tank.
e.      What is the volume andmass flow rate of the stream of water?
f.       What is thepressure of the fluid as it enters the pipe, again at the bottom ofthe tank.
