Calculate the total available energy from a water stream by use of a turbine?

[bobmurray1]

I keep confusing myself on this question, basically i want to know how you would determine the amount of potential energy you could capture by using a turbine, if water is flowing down a pipe into a river.

The change in elevation from the start to end of pipe is 30 meters.
The pipe is 100 meters long.
Water is flowing at a rate of 10 liters per second.

Not assuming the efficiency of the water turbine itself, is the formula just the potential energy minus the friction in the pipe? Thus:
Power per time = (Mass Flowrate X Gravitational constant X Change in Elevation) - Friction losses
= ((10 L/s X 0.001 m3/L X 1000 kg/m3) X (9.81 m/s2) X (30 m)) - Friction
= (2943 W/s or 2.94 kW/s) - Friction

Also second question, I know how to calculate the friction in a pipe, but the problem i cannot get my head around is that because the pipe is nearly a meter in diameter, the pipe is not full of water, thus i dont know how to calculate Reynolds number etc? Any help here would also be appreciated,

Thanks Guys

 

[LittleInch]

If your pipe is not full of water then your calculation is flawed as you have no static head and all the potential energy is being dissipated along the pipe. You need to reduce the flow out so that the flow in equals or exceeds the flow out and fills up the pipe from one end to the other. Only then will you have the potential energy to draw on via a turbine.

All you have at the moment is a very small amount of kinetic energy.

Beware that turbine / pump efficiency to electric is about 60% at best.

Also be careful with your units. J/sec are Watts. You are mixing up energy with power, which is energy per second and volume should be in m3.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[bobmurray1]

Thanks for the reply!

I understand what you are saying, but i dont understand why it would not work? Surely, if water is flowing down an elevation of 30m along a pipe, full or not, it still has the static head of 30m?

Im just not fully grasping the concepts here, as most calculations i have worked with before have been when the pipe is full.

Are you trying to say that all the potential energy from the water elevated 30m is dissipated as it travels down the pipe because the pipe is not full?

And yeah, my mistake on the units.

Thanks!

 

[DRWeig]

Are you trying to say that all the potential energy from the water elevated 30m is dissipated as it travels down the pipe because the pipe is not full?

Yes.

If your pipe isn't full, you have 30 feet of air in your pipe, plus some water traveling through it. The pressure difference or static head is equal to the difference in air pressure from top to bottom (not much). The pressure difference of the water from top to bottom can't be any greater than the pressure difference of the air. Without the air, the weight of the water in the pipe determines the static head.

The kinetic energy of the mass of water flowing is due to the elevation, so your static head is already used up.

All you can recover is (part of) the kinetic energy of the water, same as if a stream were flowing across the bottom of a paddlewheel. The only pressure it exerts is velocity pressure.



Best to you,

Goober Dave

Haven't see the forum policies? Do so now: Forum Policies

 

[LittleInch]

You have the answer right in front of you, i.e. "static" head. If your pipe was full but not flowing, then yes you have at the base of that pipe water with a pressure of about 3 bar. If you open a valve and draw off water at the same or less flow than still comes into the top then the pressure at the bottom will be 3 bar minus friction in the pipe. You can do something with that pressure.

However, if you draw off water at a faster rate than is coming in, then eventually the pipe has only flowing water and air pressure and at the end the pressure gradually falls to air preassure and you have created an artificial river. The potential energy of the water has been transferred into kinetic energy due to the velocity of the water which at a fall of 30m in 100, will be going pretty quickly and all eaten up by the friction losses in the pipe

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way