How to Calculate Electrical Power from Water Flow Rate?

[calbolan]

Hi,

Me and 4 others are stumped on our HNC Electrical Project. We need an equation that calculates from the flow rate of water and diameter of a pipe, what amount of electrical power outage can be gotten by using a simple turbine connected to the pipe.

Any sort of help would be greatly appreciated as we are more than struggling with the whole of this project.

Regards,

Cal

 

[deep838]

I guess Bernoulli's principle could be a starting point if velocity is required...
It states that the sum of the potential energy, kinetic energy and the pressure energy is constant...
So:
$\frac{1}{2}$mv² + mgh + PV = constant

So, if the initial energy be known, we can compute the velocity and hence the rate at which the water is flowing.

 

[rude man]

Mass flow rate = dm/dt = ρ dV/dt = ρ v A, solve for v.

v = flow velocity along pipe in m/s
ρ = density, kg/m^3
A = pipe area in m^2
dm/dt = mass flow rate in kg/s
dV/dt = volumetric flow rate in m^3/s = vA

So in 1s the delivered K.E. would be 1/2 dm/dt v^2

Make sense? Not my main field but seems straightforward.

 

[InquisitiveOne]

Hi,

Me and 4 others are stumped on our HNC Electrical Project. We need an equation that calculates from the flow rate of water and diameter of a pipe, what amount of electrical power outage can be gotten by using a simple turbine connected to the pipe.

Any sort of help would be greatly appreciated as we are more than struggling with the whole of this project.

Regards,

Cal

Hey Cal,

Per the forum rules, I can not offer any help without proof that you've attempted to figure it out on your own. Perhaps you can share some specific details about your inquiry and particular steps you've taken to solve your question?

What is the total head?
Pipe ID?
Pipe length?
Simple turbine? What kind? Turgo, Pelton, Kaplan, Banki... Water wheel?

 

[Nickie]

vin

Hi Calvin,

I understand your struggle and I am happy to help. The equation you are looking for is called the hydraulic power equation. It is used to calculate the power output from a turbine based on the flow rate of water and the diameter of the pipe it is connected to. The equation is as follows:

P = Qρgh

Where:
P = power output (in watts)
Q = flow rate (in cubic meters per second)
ρ = density of water (in kilograms per cubic meter)
g = acceleration due to gravity (9.8 m/s^2)
h = height difference (in meters)

To use this equation, you will need to know the flow rate of water in cubic meters per second. This can be measured using a flow meter or calculated using the velocity of water and the cross-sectional area of the pipe.

Next, you will need to know the density of water, which is approximately 1000 kg/m^3.

You will also need to measure or calculate the height difference between the water source and the turbine. This could be the height of the water source above the turbine or the height of the turbine above the water level.

Once you have all of these values, you can plug them into the equation to calculate the power output of your turbine. Keep in mind that this is the theoretical maximum power output and may not account for losses due to friction and other factors.

I hope this helps and good luck with your project! Let me know if you have any further questions.

Best,