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# Velocity through a water turbine

## Velocity through a water turbine

(OP)
Hi all

I have a question about calculating power from a water turbine.  If I have a rotor with an inlet area A1 and an inlet velocity V1, and an outlet area A2 and velocity V2, if the rotor tapers down, A2 is smaller than A1, therefore to satisfy the mass flow rate through the closed rotor, V2 (axial) must be greater than V1 (axial).  But... for a water turbine I understand that V2 needs to be smaller than V1 as work is done and hence the dynamic pressure must decrease, not increase.  I'm calculating the power at the inlet of the rotor and the outlet of the rotor using Power = the flow rate (Area x velocity) multiplied by the dynamic pressure (0.5 x area x density x velocity2 ).  My issue is if I use axial velocity, which satisfies the mass flow rate, I get negative power as work is done on the liquid to increase the velocity.  If I use the total velocity component (using CFD) in this equation, I get what seems a realistic power but the mass flow rate in is much greater than the mass flow out.  Please help me!  I am utterly confused!

Also, as I mentioned, the turbine I'm working on has a decreasing cross sectional area through the rotor... is it just me, or is this silly?  Aren't you better with an increasing area through the rotor?  I'd be interested in anyone's thoughts on this.

Thank you,

Kat

### RE: Velocity through a water turbine

Hi katmech

Check your units if you have:-

Area x velocity) multiplied by the dynamic pressure (0.5 x area x density x velocity2 ).

Power should be N*m/s from your units above unless I am making a mistake I can't get N*m/s.

formula I was looking at was :-

mass flowrate *(V-v)*v     where V,v are the initial and
final velocities of the jet
respectively normal to the vane

thats the power output formula for jets on to a rotor with flat plates.

desertfox

### RE: Velocity through a water turbine

(OP)
Sorry desertfox, my mistake, the dynamic pressure is 0.5 x density x velocity^2, it doesn't include the area.  The units work out to be Watts with this dynamic pressure multiplied by the flow rate (area x velocity).  The text books I have, and previous reports use this equation for the water turbine I'm looking at, but they just say to use the velocity, and don't specify if this is the velocity parallel to the turbine axis, or the total velocity component of the water exiting the turbine.  Obviously as the water has just past through the turbine, it has a large angular component to the velocity so the total velocity is very different from the parallel velocity component.  So, which one should be used in this power calculation?  Any ideas?  Thanks!

Kat

### RE: Velocity through a water turbine

hi katmech

Its difficult to say of the description you give any chance of uploading a file of what your looking at.

desertfox

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