Radius of gyration/power/rev per minute

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Homework Help Overview

The discussion revolves around a problem involving a water wheel that generates power from flowing water. The original poster attempts to calculate the mass of water impacting the wheel to produce a specified power output and to determine the rotational speed of the generator based on given parameters such as radius of gyration and mass.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of potential and kinetic energy in relation to power output, with some questioning the correctness of their mass calculations. There is also exploration of the relationship between kinetic energy and rotational motion, with references to relevant equations.

Discussion Status

Some participants have provided guidance on the equations to use for kinetic energy and power, while others express uncertainty about the application of these equations and the need for specific constants. The discussion reflects a mix of attempts to clarify concepts and calculations without reaching a definitive conclusion.

Contextual Notes

Participants note the importance of units and the lack of a time element in the energy calculations, which may affect the ability to derive certain values. There is also mention of the original poster's uncertainty regarding the use of specific values and constants in their calculations.

tommy56
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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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