Force of Fluids

n_h0987

1. The problem statement, all variables and given/known data

A fresh water pond that is 16.4 m deep is contained on one side by a cliff. The water has eroded a nearly horizontal "tube" through a bed of limestone, which allows the water to emerge on the other side of the cliff. If the "tube" has a diameter of 3.17 cm, and is located 5.5 m below the surface of the pond, what is the frictional force between the "tube" wall and a rock that is blocking the exit?


2. Relevant equations

pressure of fluid = pressure at surface + (density of fluid x g x depth)


3. The attempt at a solution

pressure of water at a depth of 5.5 m = 1.013*10^5 Pa + (1000kg/m^3 x 9.81 N/kg x 5.5 m)
= 155 255 Pa

Since the pressure of a fluid is the same at the same depth, I figured that the pressure of the water inside the tube is also 155 255 Pa. Since the rock is not moving, the force of the water must be equal to the frictional force.

Force of water = pressure x area of end of tube
= 155 255 Pa x (pi x 0.01585^2)
= 123 N