# Energy changes of water from a reservoir

1. Oct 28, 2015

### Janiceleong26

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

2. Relevant equations

3. The attempt at a solution
I know that the water loses gravitational p.e. as it flows down, and since it flows through the pipe at a constant rate, v does not change, so k.e. remains the same. It left me stranded with B or D. The answer is B. What does elastic potential energy got to do with this situation? Does it got to do with increase in pressure? If so, how does pressure relate to elastic p.e.?

2. Oct 28, 2015

### SteamKing

Staff Emeritus

Is the water in the reservoir traveling at any velocity before it enters the pipe? Is the K.E. of the water in the reservoir the same K.E. of the water flowing out of the pipe at the bottom? Is water an elastic substance?

3. Oct 28, 2015

### Janiceleong26

K.E of water in the reservoir is 0, K.E. of water entering the pipe = K.E. of water flowing out of pipe. But the question is asking for the change in energy of the water as it flows from X to Y.. Not from the reservoir to bottom of pipe :/
Water is not an elastic substance

4. Oct 28, 2015

### phoenix95

correct.
Not correct.

5. Oct 29, 2015

### Janiceleong26

Hmm..but I thought the water is flowing at a constant rate, which means constant v, thus constant K.E. throughout the pipe and to the turbine? :/

6. Oct 29, 2015

### phoenix95

Answer this, does water loose gravitational potential energy during the flow?

If it does, then where does it re-appear? In what form? Then you may find out if the statement below is right or wrong.
A hint: You said that the kinetic energy of the water in the reservoir is zero. The water entering the point x should have no kinetic energy then.

7. Oct 29, 2015

### Janiceleong26

Yes it loses gravitational p.e.
It gains K.E.?

8. Oct 29, 2015

### phoenix95

OK, This is what I thought...
Water is an incompressible fluid, which means it can't be deformed under stress. So elastic potential energy has no business here.
It definitely loses gravitational potential energy which has to appear as kinetic energy of the fluid.

9. Oct 29, 2015

### Janiceleong26

Yeah, that is what I thought too..
This is the examiner report :

How does the increasing pressure between X and Y leads to a gain in elastic p.e. ?

10. Oct 29, 2015

### phoenix95

I can only explain it like this...
Let us assume that the water flows at constant rate along the pipe (which I think is not true , because the flow would be turbulent), then the kinetic energy is constant.
But the pipe is sealed off, so the water at the end of the pipe experiences pressure. I think this is what they referred to as 'Elastic potential energy being developed'.
Elastic potential energy is potential energy stored due to the deformation of an elastic object. Since water is incompressible there can be no such thing in this case. However, one can say that water develops energy due to pressure.
Or in other case the sealed end wall of the pipe is elastic. In this case the wall deforms and hence the elastic potential energy increases.

I think the problem lacks information, otherwise puts in too much conditions (no offense). The problem clearly states that the water flows through the pipe and through the turbines. But the examiner says the pipe is sealed off.

11. Oct 29, 2015

Haha ok