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.

 

[rwisz]

I would like to clarify a few things about the given information and the questions asked. Firstly, it is important to note that the radius of gyration, power, and revolutions per minute are all different concepts and cannot be directly related to each other without more information.

The radius of gyration is a measure of the distribution of mass around an axis of rotation. It is calculated by taking the square root of the moment of inertia divided by the total mass. In this case, the given information does not provide enough information to calculate the moment of inertia or the total mass of the water wheel and generator system.

Power is the rate at which work is done or energy is transferred. It is measured in watts (W) or kilowatts (kW). In this case, the given information states that the water wheel is producing 20 kW of power. However, it does not specify the efficiency of the system, which is necessary to calculate the mass of water hitting the wheel per second.

Revolutions per minute (RPM) is a measure of rotational speed and is commonly used to describe the speed of rotating objects. In this case, the given information provides the radius of gyration and mass of the water wheel and generator system, but it does not specify the torque or angular velocity, which are necessary to calculate the RPM.

In order to accurately calculate the mass of water hitting the wheel per second and the revolutions per minute of the generator, we would need more information about the system such as the efficiency, torque, and angular velocity. Without this information, it is not possible to provide a response to the given content.