Energy in a free vortex of water

[pheonixrider]

Hey guys,

I'm actually working on a project of gravitational vortex turbine at an undergrad level. I need to know the energy or the energy required to make a stable free vortex in a cylinder. The cylinder is of 1 m height and 1.5 m diameter. A channel of 0.5 m width is connected to the cylinder. The flow enters into the cylinder tangentially and leaves through an orifice at the bottom of 0.1 m diameter.

Any help would be appreciated.

Thanks.

 

[HuskyNamedNala]

As a rough approximation if you have the vortex velocity profile you can integrate it to obtain the power and then estimate the kinetic energy. Recall P = dE/dt = F dot(v) = dv/dt dot(v). You can estimate the power per unit cross section if you take an imaginary slice parallel to the rotational axis.

 

[HuskyNamedNala]

forgot the mass term, sorry