5.5.2 Power, head and flow rate
The power supplied by a plant, (the number of watts), is the rate at which it delivers energy: the number of joules per second. In a hydro plant this will obviously depend on the volume flow rate of the moving water - the number of cubic metres (m3) per second passing through the plant, usually represented by the symbol Q (think ‘Quantity’).
It then follows from the equation shown in Figure 10 that this power will be:
However in any real system the water falling through a pipe will lose some energy due to frictional drag and turbulence, and the effective head will be less than the actual or gross head. These flow losses vary greatly - in some cases the effective head is no more than 75% of the actual height difference, in others as much as 95%.
Then there are energy losses in the plant itself. Under optimum conditions, a hydroelectric turbo-generator is extremely efficient, converting all but a few percent of the input power into electrical output. Nevertheless, the efficiency (the ratio of the output power to the input power) is always less than 100%. With these factors incorporated, the output power becomes:
Note that although efficiency is often quoted as a percentage, in an equation like this it will be a number between 0 and 1. For example, 85% becomes 0.85.
So, moving on, if we now express P in kilowatts, and use the approximation g = 10 m s–2, we obtain a very useful simple expression:
Now you know how to work out how much power a plant can supply, we will now move on in the next section to look at the types of hydroelectric plant.