Water Flow - Different Amount of Energy From The Same Potential Source?

Question

When calculating the amount of power available from a water outlet (using a system that converts the kinetic energy of the water flow to power with for example a Pelton wheel), the energy per unit time is different depending on the nozzle size and hence flowrate of the water leaving the outlet.

In a hypothetical perfect system where total volume of water out is the same regardless of nozzle diameter (but hence the speed varies inversely with nozzle area), how is it that more energy is available ($\frac{1}{2}mv^2$) at higher speeds, when surely the potential energy in the system is a very specific fixed value.

Of course in reality the mass flowrate will reduce with nozzle area reduction - but hypothetically I don't understand why there is an apparent difference in energy potential between the configurations.

Answer 1

how is it that more energy is available ($\frac{1}{2}mv^2$) at higher speeds, when surely the potential energy in the system is a very specific fixed value.

You are only accounting for the potential energy and kinetic energy of the flow and neglecting pressure energy (see Bernoulli equation). There is a lowering of pressure in the constriction. In the high velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy.

For more details, see http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html

Hope this helps.