Question

A shallow well usually has the pump at the top of the well. (a) What is the deepest possible well for which a surface pump will work? [Hint: A pump maintains a pressure difference, keeping the outflow pressure higher than the intake pressure.] (b) Why is there not the same depth restriction on wells with the pump at the bottom?

Short answer

Answer: The maximum depth for a pump at the top of a well to work is approximately 10.3 meters. This is because the pump has to maintain a pressure difference equal to atmospheric pressure to lift the water column. On the other hand, a submersible pump placed at the bottom of the well does not have to maintain this pressure difference since it is submerged in the water and can push water directly up the pipe. This eliminates the depth restriction that exists with a surface pump.

Step-by-step solution

Understand key concept

A pump works by creating a pressure difference between the inflow and outflow, allowing water to be pushed up. This pressure difference is restricted to 1 atmosphere (atm) to prevent the formation of a vacuum on the inflow side.

Calculate the pressure in the water column

At the surface of the well, the pressure is equal to atmospheric pressure. To find the maximum possible depth for the pump to work, we need to know the pressure at the bottom of the water column. The pressure in the water column is given by the formula: Pressure = Density of water * Gravity * Depth Density of water = 1000 kg/m^3 (approximately) Gravity = 9.81 m/s^2 We want to find the maximum depth that would maintain the pressure difference of 1 atmospheric pressure. 1 atmospheric pressure is equal to 101325 Pa.

Find the maximum depth

Now we can find the maximum depth of the well (D) by rearranging the pressure formula and solving for D: D = Pressure / (Density of water * Gravity) D = 101325 Pa / (1000 kg/m^3 * 9.81 m/s^2) D ≈ 10.3 meters So, the deepest possible well for which a surface pump will work is approximately 10.3 meters.

Why there isn't a depth restriction with a submersible pump

In the case of a submersible pump placed at the bottom of the well, the pump does not have to maintain a pressure difference equal to atmospheric pressure because it is submerged in the water. Therefore, it can push water directly up the pipe without having to lift the entire water column. This eliminates the depth restriction that exists with a surface pump.