Calculate the rate of potential energy loss of water in a pipe

[kwal0203]

Homework Statement

Question: what rate does the water lose gravitational potential energy?

Data:
I have a pipe that water is flowing through and the pipe has 2 sections.

In section 1:
- the pipe is 11.9m above section 2 so, h = 11.9m
- the velocity of water is $$v_1 = 0.3240ms^{-1}$$
- pressure is 1.126atm
- radius is 0.5530m

Section 2:
- the velocity of water is $$v_2 = 1.390ms^{-1}$$
- pressure is 2.268atm
- radius is 0.2670m

Density of water: $$\rho_w = 1000kgm^{-3}$$
Viscosity of water: $$\eta = 8.90 \times 10^{-4} Pa s$$

Homework Equations

Gravitational potential energy: U = mgh

The Attempt at a Solution

Haven't gotten far with this. My first instinct was to find U, so I did this:

volume flow rate times density $$= 0.311m^{3}s^{-1} \times 1000kgm^{-3}$$
$$= 311kgs^{-1}$$

$$U = 311kgs^{-1} \times 9.8ms^{-2} \times 11.9m$$
$$ = 36268.82J$$

I'm not sure if what I've done so far is valid but I seem to have 36268.82J of potential energy in one seconds worth of water flow.

Not sure how to proceed here to get a rate of potential energy loss. Hopefully I can get some help how to think about this. Any help appreciated thanks.

 

[Chestermiller]

The water flow is downward, correct?

 

[J Hann]

You wrote U = 36268.82J
Shouldn't it be U / t = 36268.82 J / sec?