Parallel Pipe Flow: Potential Energy Drop

[Soaring Crane]

Let us consider the following scenario. Water is pumped to high pressure, but the water then faces a fork in the pipe. Two pipes lead back to the pump: large pipe L and small pipe S. Since the water can flow through either pipe, the pipes are said to be in parallel. Since this is so, the overall flow of water that enters the system before the fork is equal to the sum of the flows through L and S.

What can be stated about the drop in potential energy (per unit mass or volume) of water traveling through either pipe?

a. The drop is greater for pipe L.
b. The drop is greater for pipe S.
c. The drop is the same for both pipes.

Is the answer a? Since there is a a greater flow of water in the large pipe, there is a greater mass of water for potential energy? Is this right at all? If not, please explain the correct choice to me.

Thanks.

 

[BobG]

Since it's potential per unit of mass, then the fact that there is more mass doesn't matter.

Water follows path of least resistance. If it became harder to go down one pipe than the other, where would most of the water try to go, at least until there were so much water going down the 'easy' pipe that the first pipe now became the easier path, and so on and on and on. One path can never end up taking more potential energy per unit of mass than the other - they have to stay equal.

 

[Soaring Crane]

Consider another circuit: water is pumped to high pressure and fed into only one pipe. The pipe has two distinct segments of different diameters; the second half of the pipe has a smaller diameter than the first half.

Which of the following statements about the flow and change in pressure through each segment is true?

A) The flow through each segment is the same as the overall flow; the change in pressure through each segment is the same as the overall change.
B) The flow through each segment is the same as the overall flow; the sum of the changes in pressure through each segment equals the overall change.
C)The sum of the flows through each segment equals the overall flow; the change in pressure through each segment is the same as the overall change.
D) The sum of the flows through each segment equals the overall flow; the sum of the changes in pressure through each segment equals the overall change.

I think the answer is either C or D, but I am unsure about the pressure part. Is conservation a key player here like the latter part of choice D for pressure?

Thanks.

 

[BobG]

Try comparing it to an example people are more likely to be familiar with - electricity. Your first example is a parallel circuit. Your second is a series circuit.

In the parallel circuit, there's more water on the side with least resistance (the wider pipe). The total amount of passing through both pipes is the equal to the amount of water in the single pipe before the fork. Because water, like electricity, follows the path of least resistance, the amount of water in each pipe would balance out to keep the potential energy constant.

In the series circuit, your overall water flow has to remain the same (the water in the wide pipe eventually has to go through the narrow pipe so total amount of water flowing in the wide pipe can't be greater than the amount flowing through the narrow pipe). The resistance (and pressure) in the narrow pipe is greater, meaning you drop more potential energy getting through it than you do the wide pipe (just like you drop more voltage crossing a larger resistor).

 

[Soaring Crane]

So, basically:

H2O in wide pipe = H2O in small pipe = overall flow

and since each pipe has a different change in pressure, the sum of these changes equals the total pressure or B?

 

[BobG]

Yep, in fact double yep (just to meet the minimum character requirement).