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Pipe sizing example:
A site has 50 meters of head and a flow of 5 liters per second, a very typical situation here on the coast. The pipeline will have to be 150 meters long, and is going to be polyethylene plastic, (poly pipe). We will accept a head loss of 10% at maximum flow, that is, 5 meters of height lost to pipe friction. The power line length is 50 meters to the battery.
Refer to the section on "Power Calculations" for more detailed explanations of these formula.
Step 1.
Determine the available power.
5 liters per second is 0.005 cubic meters per second )
Power = ( 1000 x Q x h x 9.8 ) x efficiency) watts
Power = ( 1000 x 0.005 x 50 x 9.8 ) x 0.5 ) watts
Power = ( 5 x 50 x 10 ) x 0.5 = 1250 watts
Note: the acceleration due to gravity value of "9.8" was rounded up to "10"
The final output will be somewhat less as the net head will be 45 meters at full flow, or around 1125 watts, 90 % of the last calculation. This is close enough, and we decide to proceed with the project.
Step 2.
Plot a flow of 300 liters per minute on a friction chart applicable to the pipe material you are using, so the flow velocity is less than 5 feet per second. Note the pipe size indicated, and draw lines for several sizes that are available. This will likely be 2 inch, 2.5 inch, 3 inch and 4 inch.
Pipe friction charts are available from pipe suppliers. Each type of pipe will have a different coefficient of friction, so a chart used for steel will not be accurate for plastic pipe.
From the chart ...
2 inch gives a velocity of 8.2 feet per second which is too fast.
2.5 inch results in 5.2 feet per second.
3 inch gives 3.7 feet per second.
Pipe inside diameters vary with pipe schedule, (wall thickness), so you will seldom get exactly the diameters listed. Adjust the line you drew on the graph to match the pipe diameter you will be using. This is extremely important if you are using small diameter pipe like 1 inch or 1.25 or 1.5 inch PVC. Some pipe is sold by schedule and some by 'DR' rating (dimension ratio). On long runs of 1000 feet, even the slight differences in inside diameter can make a big difference to head loss. Be careful when making calculations.
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If you really want to know the PVC pipe loss, here is the standard 'Hazen-Williams' formula that is used for pressure pipe friction loss. You can also Google it to find more information on the subject.
f= 0.2083 (100/C)^1.852 X Q^1.852 / id^4.865
where f = friction loss per 100 feet
C = coefficient of friction, usually 150 for PVC
Q = water flow in USGM
id = pipe inner diameter
For Poly pipe, C is often 140 meaning higher friction. Always try to find out the C for your pipe and the exact id.
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Our allowable head loss is 5 meters in 150 meters of pipe length, or 3.33 meters per 100 meters of pipe. Charts are usually normalized to meters per 100 meters or feet per 100 feet, so you may want to convert at this point. In this example, 2.5 inch poly pipe will deliver the required maximum flow with 3.3 meters of head loss per 100 meters of pipe, and the flow velocity is right on 5 feet per second.
It is possible to run more water through the 2.5 inch pipe by increasing the nozzle size. This will increase the head loss beyond our limits, but it will produce more power. In fact we could drop to 70% of the gross head before the power curve would start to fall. However, wide ranges of pressure result in variable jet velocities which in turn determine turbine RPM. In DC systems this is often acceptable, but in AC systems, RPM must be maintained, and a low jet velocity results is a significant loss of efficiency. This is why hydro equipment is so site specific, what worked well at one site may perform badly at another.
Step 3.
Determine the correct nozzle diameter to accept a maximum of 5 liters per second. Often, several nozzles are cut and installed to match flow conditions. 'Stream Emgine' turbines used on some of the example sites featured here are equipped with 2, 3 or 4 nozzles. Each nozzle can have a control valve permitting a wide range of flow to suit conditions. In larger AC systems, spear nozzles are often used which permit continuous adjustments of flow by varying the position of a movable spear within the nozzle.
Refer to a nozzle flow table to determine the correct size to use, or start small and gradually increase the size while measuring the flow in a bucket or through a weir.
Since water is non compressible, the flow velocity and nozzle size can be calculated from scratch. One only needs these formulas. The flow will typically be 5% less than the jet area suggests, so cut it a fraction big. Also, jet velocities are often about 5% less than calculated due to inefficiencies in the nozzle and other complex factors.
Area = 3.1428 x R^2 (Radius)
Circumference = 3.1428 x D (Diameter)
Jet velocity = 8 x H ^ 1/2 ( 8 times the square root of the net height in feet)
Imagine a solid bar of water passing through the nozzle traveling at the jet velocity. One only needs to determine the bars volume per unit time as it passes by. This is usually in one second. The diameter and hence cross sectional area are found first, then simply multiply this by the 'bars' length passing per second to arrive at the volume. This is easy to do in cubic inches and linear inches, then convert to gallons or litres. See the conversion chart below.
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