Penstock head loss calculation

Am I right in thinking that as it's a hydro plant the penstock is a pipe or duct taking water to the turbine? (It's something completely different in say a sewage treatment works) If so, the normal pipe friction loss calculations apply.

Codey

I'm currently working in a small hydro scheme where the head is low (4m). I looked into the losses in pipes associated with carrying the water to the turbine, trying to find an optimum for the topography. i.e. I was exploring the relationship between longer pipe runs and head gained by going further up the valley. I used my old fluid mechanics text book. You'll be able to find the same formulae if this is what you require. I played around with pipe diameter and flow on a spreadheet.

Naturally the cost of the piperun forced the decision in the end!!

Dear All,

Thank you very much for your valuable advice. My profession I'm an Electrical Engineer, so I'm not very much conversant with those formulas. So could you pl help me to proceed?

Our circular penstock is made of spirally welded steel plates (OD = 1. m, t = 10mm, length 1500m) and internal was painted with epoxy paint.

Through the internet I found a formula to calculate head loss in a straight pipe (www.engineeringtoolbox.com/hazen-williams-water-d_797.html), to apply that formula I need to know the following parameters.

Design coefficient (C)

Hydraulic diameter (Dh), What could be the values I can use for this particular penstock?

Also there are around 30 bends in our line, and all those bends were fabricated with pipe pieces to make it smoother. What is the equation where I can apply to find out losses in those bends?

I used the 'trial and error' method as mentioned in the link, so i'm afraid I don't know but any method must refer to Reynolds number or turbulence in some way. I didn't worry about bends either as the installation would be able to avoid tight ones. I'll try to dig out the formula.

Following your link gave C = 150 for plastic, but this is very smooth, and if your pipe is rougher a smaller C might be appropriate. I'm sure figures for various materials are on the web somewhere. For a circular pipe, Dh = ordinary (inside) dia. 0.98m in this case.

But I wouldn't use Hazen-Williams, I use formula expressing headloss as multiple of velocity head V²/(2*g). So headloss = K*V²/(2*g). For straight pipe, K = 4*f*L/D. Strictly speaking, f depends on pipe roughness and Reynolds No., but if you take f = 0.005 you're unlikeky to be far out. So K = 4*0.005*1500/0.98 = 30.6. For bends, K ~ 0.3 each giving K = 9. Total K = 39.6, say 40.

You don't give flow or velocity, but if it's a reasonable 1 m/s, V²/(2*g) = 0.051m so headloss = 40*0.051 = 2.04m.

Trust this helps......Codey

Dear Sir,

Thank you all for your generosity. With your valuable help I managed to calculate penstock loss in line.

What about if you see an Hydraulics Handbook?

In Mexico some of we use Sotelo Avila´s book as reference and as reference of references.

good luck