Hey there, im having a slight issue understanding a few concepts, il explain the scenario first.
Imagine a 60 cm diameter cast iron pipe which is 100 meters long with a change of elevation of 50 meters from start to end of pipe. 100 litres per second of waste water is fed into the start of the pipe, and i want to calculate how much energy could be produced by implementing a turbine at the end.
Assuming the pipe is full of water from start to finish, what would be the best way of calculating the potential power by use of a turbine? Also how could i ensure that the pipe remained full of water, thus the 100 liters per second of water flowed through the turbine?
This is what i have been thinking as an initial calculation (not including turbine efficiency or loss of head due to friction):
Power = mgh = (100 kg/s) X (9.81 m/s2) X (50 m) = 49050 W or 49 kW
Obviously as the pipe diameter is quite large, id assume it would have to be reduced before entering the turbine. But i cannot get my head around how the flowrate within the pipe can be made to be a constant at 100 litres per second, any less and the water in the pipe will reduce, any more and the water will overflow?
The only thing i can think of is because the head and flowrate is set, the diameter at the discharge end of the pipe must be changed to suit? But im unsure how you can calculate that, and also adding the turbine would affect head loss, changing the diameter?
Any help would be greatly appreciated, im stumped right now!
Water Turbine Calculations
Re: Water Turbine Calculations
Actual flow rate you can calculate based on the height difference and pipe diameter that you have. You can't tell at the start that you will have 100 l/s. That you can calculate. Here is report from calculation using pressure drop calculator:
Pipe pressure drop calculator
1. volume flow rate (q):
q : 14.303537 l/s
3. pipe length (L):
L : 100 m
4. pipe diameter (D):
D : 60 mm
5. pipe roughness (kr):
kr : 0.1 mm
6. density (ρ):
ρ : 1000 kg/m3
9. K factor  minor losses coefficient (K ):
K : 0.0
10. velocity (V):
V : 5.0588536 m/s
12. friction coefficient (f):
f : 0.022999486
16. pressure drop (p1p2):
p1p2 : 50 mWS
so with 60 mm pipe and 100m long pipe and 50 m of height difference you have only 14 l/s. So flow rate is defined by energy in terms of water height and that energy is used for friction losses compensation. That friction allows only 14 l/s of water flow. With 14 l/s all water energy of 50 m of water is consumed. If you want more flow, you must increase pipe diameter, or put more energy  make more water height.
On the pipe exit you have flow kinetic energy. Energy per unit of mass you can calculate like v^2/2 [J/kg]. From there you can also calculate energy per second [W] like v^2 * G/2 (G  mass flow kg/s). Velocity for 14 l/s is 5,05 m/s and mass flow is 14 kg/s, leading to P = 5,05^2 * 14 / 2 = 179 W.
Pipe pressure drop calculator
1. volume flow rate (q):
q : 14.303537 l/s
3. pipe length (L):
L : 100 m
4. pipe diameter (D):
D : 60 mm
5. pipe roughness (kr):
kr : 0.1 mm
6. density (ρ):
ρ : 1000 kg/m3
9. K factor  minor losses coefficient (K ):
K : 0.0
10. velocity (V):
V : 5.0588536 m/s
12. friction coefficient (f):
f : 0.022999486
16. pressure drop (p1p2):
p1p2 : 50 mWS
so with 60 mm pipe and 100m long pipe and 50 m of height difference you have only 14 l/s. So flow rate is defined by energy in terms of water height and that energy is used for friction losses compensation. That friction allows only 14 l/s of water flow. With 14 l/s all water energy of 50 m of water is consumed. If you want more flow, you must increase pipe diameter, or put more energy  make more water height.
On the pipe exit you have flow kinetic energy. Energy per unit of mass you can calculate like v^2/2 [J/kg]. From there you can also calculate energy per second [W] like v^2 * G/2 (G  mass flow kg/s). Velocity for 14 l/s is 5,05 m/s and mass flow is 14 kg/s, leading to P = 5,05^2 * 14 / 2 = 179 W.
Pipe flow calculations  since 2000
Re: Water Turbine Calculations
very informative post, thanks for the help and sharing

 Posts:1
 Joined:Wed Apr 02, 2014 8:27 am
Re: Water Turbine Calculations
If you can calculate the actual flow rate of the pipe, then you can get the dimension and length required also these info will help you to prepare a quick data about the flow rate. So by managing the length and the height you can control the flow rate as well as increase the production.