Radius of gyration/power/rev per minute

[tommy56]

Homework Statement

A water wheel rotates a generator producing power from vertically flowing water onto its blades. Height of water is 100m above blades. init vert velocity is 0.
I have calc velocity at hitting wheel as 44.3m/s
calc the mass of water hitting the wheel per second to create 20kW power
Calc rev/min of gene (wheel and gene combined radius of gyration 3m and mass 120kg)

Homework Equations

v²=u²+2as
K.E=0.5mv²
P.E=mgh
J=mk²
g=9.8m/s²

The Attempt at a Solution

For mass I have calculated P.E and K.E in terms of m and made equal to 2000 giving answer 10.2Kg? not sure if this is right.
For rev/min I have worked out J=120x3² = 1080kg m², not sure where to go from here?

 

[rock.freak667]

The Attempt at a Solution

For mass I have calculated P.E and K.E in terms of m and made equal to 2000 giving answer 10.2Kg? not sure if this is right.
For rev/min I have worked out J=120x3² = 1080kg m², not sure where to go from here?

10.19 or 10.2 kg/s is correct. Remember to put the correct units of mass per second.

For the second part, remember that you can the kinetic energy of a rotating component as E = Iω² = mk²ω².

or in terms of power P = Mk²ω² where M is the mass per second and ω is in rad/s.

 

[tommy56]

10.19 or 10.2 kg/s is correct. Remember to put the correct units of mass per second.

For the second part, remember that you can the kinetic energy of a rotating component as E = Iω² = mk²ω².

or in terms of power P = Mk²ω² where M is the mass per second and ω is in rad/s.

Thanks for the help, but I cannot find that equation, I can however find the equation E = 0.5 mk²ω².
If I use this then I get 20000=0.5x120x3²ω²
which gives me 6.086rad/s.
Am I right to use the mass of 120kg, as this is given in the question, and I'm not sure if i need the 0.5 in the equation? Thanks.

 

[rock.freak667]

Thanks for the help, but I cannot find that equation, I can however find the equation E = 0.5 mk²ω².
If I use this then I get 20000=0.5x120x3²ω²
which gives me 6.086rad/s.
Am I right to use the mass of 120kg, as this is given in the question, and I'm not sure if i need the 0.5 in the equation? Thanks.

That's equating energy with power,

you need to find E which would normally be the KE+PE but you aren't given a time element so I am not sure if you can get it.