Radius of gyration/power/rev per minute

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The discussion revolves around calculating the mass of water hitting a water wheel to generate 20 kW of power and determining the wheel's revolutions per minute. The calculated velocity of water impacting the wheel is 44.3 m/s, leading to a mass flow rate of approximately 10.2 kg/s. Participants clarify the use of kinetic energy equations, specifically E = 0.5 mk²ω², to relate power to angular velocity. There is some confusion regarding the inclusion of the factor of 0.5 in the equations and whether the provided mass of 120 kg should be used. The conversation emphasizes the need for a time element to accurately equate energy with power in the calculations.
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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?
 
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tommy56 said:

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.
 
rock.freak667 said:
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.
 
tommy56 said:
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.
 
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