Hydroelectric Turbine Penstock Sizing

It could be as of old an open top masonary design or as I have seen recently made from wood (treated of course) the penstock needs no real drop end to end and the sides need be made just high enough to contain the expexted flow. The bottom can be made to any reasonable dimension as is required or can be accomodated by the space you have available. The bigger the bottom section the shallower it can be made it depends on the feed in point to your storage tank. If it must be a pipe galvenised steel or if money is no object stainless. Most plastics will give up fairly quickly.

The penstock cannot be an open channel. I need to maintain the head to provide enough pressure to operate the turbines efficiently. So the pipe must be sized to handle the 15 MGD and always remain full to the intake at the top of the penstock in order to maintain the head. The turbine I am using will be able to drink 15 MGD at the 10' drop in head.

MGD million gallons per day?

Yes, MGD = million gallons per day

See http://www.pipeflowcalculations.com/flowrate/index.htm this will give you an answer after you get to cubic meters per hour I recon this at 2840. this gives a pipe diameter of 220mm 10" cross check this.

Thank you very much for the link. Would you know of any plastic pipe material that would be appropriate for this application which can handle exposure to UV rays?

I'll take a gander but it is the witching hour right now and I must sign out.

Checked this and it's much too small, giving 16 m/s. At this velocity it loses 7ft head in the 10ft vertical drop. I'd have thought something more like 1 m/s.

Incidentally I hope Gusmenocal isn't expecting much power out of this, there's only ~ 23kW in the water.

Are we on the same page? 16 meters cubed per second? multiply this up to meters per hour and you get 57600 meters per hour. per day this gives 1382400. or 304128000 gals per day. Did I miscalculate some where? I like to be factualy correct and don't mind if I am proved wrong provided I learn the error of my ways.

No, 16 m/s velocity, not 16 meters cubed per second. Comes from 2840 m³/h (as in your post) in a 10" pipe.

Cheers.....Codey

Ok there guess common language different translation.

US gallons or Imperial gallons?

200 foot open channel horizontal with large excess capacity = low loss. This terminates at an open drain with 10 feet vertical path to turbine and excess capacitywith anticyclonic baffling to supress any vortexes.

In low head systems the excess capacity = extra parallel flow paths and is the analog of more parallel resistors in an electric circuit = less resistance.

If you must be piped the whole way, suggest you choose an over capacity pipe to avoid pipe transit head loss. 2 feet head loss = 20 energy lost.

Suggest you find a flow calculator online, like one of these and run some head loss scenarios versus pipe costs and available space costs.

http://www.google.com/search?hl=en&q=%22pipe+flow+calculator%22&btnG=Google+Search

PE plastic pipe should work very well as a penstock for you. You can butt fuse the lenghts together on site, very easy. Flyght (part of ITT) makes a turbine that fits directly into the pipe, kind of like a saddle fitting around the pipe. Also very easy to install.

15 million gallons a day

(56.78 million litres a day, 2.366 million litres/hour, 657 litres per second.)

This is quite a significant volume of water.

10ft static head over 200ft (3 metres over 60 metres)

Not a particularly good gradient, but here are some figures. Lets assume PE 100 SDR33.

At 1.17m/s flow velocity, 2% head/pressure loss, 900mm pipe, 15kw generator, 125,000kwh/year (less mechanical and electrical inefficiencies)

At 1.48m/s flow velocity, 3% pressure loss, 800mm pipe, 14.5kw generator, 123,000kwh/year (less inefficiencies)

At 1.88m/s flow velocity, 6% pressure loss, 710mm pipe, 14kw generator, 120,000kwh/year (less inefficiencies)

At 2.39m/s flow velocity, 11% pressure loss, 630mm pipe, 13.5kw generator, 114,000kwh/year (less inefficiencies).

At 3.02m/s flow velocity, 19% pressure loss, 560mm pipe, 12kw generator, 103,000kwh/year (less inefficiencies)

At 3.79m/s flow velocity, 33% pressure loss, 500mm pipe, 10kw generator, 86,000kwh/year (less inefficiencies)

At 4.68m/s flow velocity, 55% pressure loss, 450mm pipe, 7kw generator, 58,000kwh/year (less inefficiencies).

As the flow velocity increases the same volume of water can pass through a smaller diameter pipe, but the pressure loss increases. 10-15% pressure loss is excessive, but so too is the cost of purchasing and laying large diameter PE piping.

If a head race were constructed to shorten the pipe run to, say 80 ft, the pressure loss along the penstock would be greatly reduced.

Here are some figures for the 80ft/24m penstock.

At 1.88m/s flow velocity, 2% pressure loss, 710mm pipe, 14kw generator, 120,000kwh/year (less inefficiencies)

At 2.39m/s flow velocity, 4% pressure loss, 630mm pipe, 13.5kw generator, 114,000kwh/year (less inefficiencies).

At 3.02m/s flow velocity, 8% pressure loss, 560mm pipe, 12kw generator, 103,000kwh/year (less inefficiencies)

All the above figures are based on my own modeling, and while I believe they are accurate you shouldn't take them as anything other than an indication of head losses for different pipes.

Hope this of some assistance.

Coles [IRL]