Why can't water turbines be placed in series to reuse kinetic energy?

[Pranav Jha]

Why can't we use turbine in series so that the the remaining kinetic energy of water after passing through one turbine can be used to turn another turbine?

 

[Drakkith]

Are you sure that we don't do this?

 

[torquil]

After a turbine has extracted energy from a stream of high energy water, the water flowing out of it at the other end is less energetic (lower pressure).

So it depends on how much pressure is left in the water after flowing through each turbine, the cost of a second turbine, the efficiency of each turbine, and the cost of building more water channels from the reservoir and so on.

 

[russ_watters]

And note, a hydro turbine is generally extracting much more potential energy than kinetic energy. And you can never extract all of the kinetic energy, otherwise your water won't be moving anymore and if it isn't moving, how is it getting through a turbine?

Anyway, the constraints here are rapidly diminishing returns vs rapidly increasing turbine size (and therefore cost). For example, since kinetic energy is a square function of velocity, cutting the velocity in half extracts for you 3/4 of the starting kinetic energy in a water stream. To keep the mass flow rate constant, the output has to have twice the cross sectional area as the input. If you halve the velocity again, you again double the size of your output again but only extract an additional 1/5 (about) of your starting energy. Double the size of the output a third time and you've extracted more than 98% of your available kinetic energy.