Force of Fluids: 123N Frictional Force

[n_h0987]

Homework Statement

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?

Homework Equations

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

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

 

[anathema]

Therefore, the frictional force between the "tube" wall and the rock is 123 N. I would like to point out that there are a few assumptions being made in this solution that may not be entirely accurate. Firstly, the pressure at the surface of the pond is not necessarily 1.013*10^5 Pa, as this is the standard atmospheric pressure and may not be applicable to the specific location of the pond. Additionally, the pressure at the surface of the pond may not be the same as the pressure at the depth of 5.5 m, as the density of the water may vary depending on factors such as temperature and salinity.

Furthermore, the calculation of the force of the water is based on the assumption that the water is incompressible, which may not be entirely true. Also, the calculation does not take into account the effects of turbulence or other factors that may affect the force of the water.

Therefore, I would suggest conducting further research and experiments to gather more accurate data and make more precise calculations. This could involve measuring the actual pressure at the surface and at the depth of 5.5 m, as well as taking into account any other factors that may affect the force of the water. Additionally, conducting experiments with different types of rocks and varying the flow rate of the water could provide more accurate results for the frictional force between the "tube" wall and the rock.