Review Conceptual Example 6 as an aid in understanding this problem. Consider the pump on the right side of Figure 11.10, which acts to reduce the air pressure in the pipe. The air pressure outside the pipe is one atmosphere. Find the maximum depth from which this pump can extract water from the well.

Conceptual Example 6

Figure 11.10 shows two methods for pumping water from a well. In one method, the pump is submerged in the water at the bottom of the well, while in the other, it is located at ground level. If the well is shallow, either technique can be used. However, if the well is very deep, only one of the methods works. Which pumping method works, (a) the submerged pump or (b) the pump located at ground level?

Reasoning

To answer this question, we need to examine the nature of the job done by the pump in each place. The pump at the bottom of the well pushes water up the pipe, while the pump at ground level does not push water at all. Instead, the ground-level pump removes air from the pipe, creating a partial vacuum within it. (It’s acting just like you do when drinking through a straw. You draw some of the air out of the straw, and the external air pressure pushes the liquid up into it.)

Answer (b) is incorrect. As the pump at ground level removes air from the pipe, the pressure above the water within the pipe is reduced (see point A in the drawing). The greater air pressure outside the pipe (see point B) pushes water up the pipe. However, even the strongest pump can only remove all of the air. Once the air is completely removed, an increase in pump strength does not increase the height to which the water is pushed by the external air pressure. Thus, the ground-level pump can only cause water to rise to a certain maximum height and cannot be used for very deep wells.

Answer (a) is correct.

For a very deep well, the column of water becomes very tall, and the pressure at the bottom of the pipe becomes large, due to the pressure increment ρgh in the relation P₂ = P₁ + ρgh (Equation 11.4). However, as long as the pump can push with sufficient strength to overcome the large pressure, it can shove the next increment of water into the pipe, so the method can be used for very deep wells.

Transcribed Image Text:

Pump Reduced air pressure A B Pump