Question

In the figure, the fresh water behind a reservoir dam has depth D = 12.9 m. A horizontal pipe 5.15 cm in diameter passes through the dam at depth d = 5.14 m. A plug secures the pipe opening. (a) Find the magnitude of the frictional force between plug and pipe wall. (b) The plug is removed. What water volume exits the pipe in 4.01 h?

Answer 1

a) Pressure due to a fluid of density $\rho$ at a depth h is given by

P=hpg

g is the acceleration due to gravity

The magnitude of frictional force between the plug and pipe wall is nothing but the product of pressure at that height and area of the pipe

F=PA

A is the area of the pipe.

If the radius of the pipe then the frictional force becomes

F = πι2hpg

The pipe is at a depth h=5.14 m

Diameter of the pipe is 5.15 cm. So radius of the pipe is

5.15 T = 200 m

Density of water is

p= 1000 kg/m

Putting the values,

F=ax (5.15) ? x 5.14 x 1000 x 9.8 N 200

= 104.93 N

b) Let us find the flow rate of water through the pipe first.

Velocity of water coming out of the pipe is given by

v= 2gh = V2 x 9.8 x 5.14 m/s = 10.04 m/s

Flow rate through the pipe is

Q = Av = ar?v=ax (lb) x 10.04 m/s 200

= 0.0209 m/s

So amount of water that exits the pipe in 4.01 hr is

V = Q x 4.01 x 60 x 60) m

= (0.0209 x 4.01 x 60 x 60) m = 301.71 m