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Knight Rider

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## Homework Statement

Hi!

I'm currently working on my school project, for which I've constructed a tesla turbine, and to complete it I'll have to make some calculations on the efficiency.

As I don't want a efficiency result that depends on a generator I've decided to mount a flywheel, with measurements and weight determined, on the turbine shaft.

The plan is to calculate the flywheel's moment of inertia and then multiply it with the angular acceleration, which should equal with the torque if I'm not wrong. Then I'll calculate the output power with help of the torque and RPM.

However I'm not sure if I'm totally right... I've done some hypotethical calculations on the issue presuming that:

- the weight of the flywheel is 5 kg, that is has a diameter of 10 cm and has the shape of a solid cylinder.

- we run the turbine with a fluid pressure of 1 BAR.

- that we register the shaft's current RPM every 0,5 second with the help of a tachometer with the following result: 1050 RPM, 1100 RPM, 1150 RPM

## Homework Equations

Moment of inertia of the flywheel: I = 0,5 x m x r

Angular velocity of the flywheel: 2pi x (RPM/60)

Angular acceleration of the flywheel: deltasomethingvalue/time = rad/s^2

Torque of the turbine: moment of inertia x angular acceleration = torque

Average power output of the turbine between 1050 RPM and 1100 RPM with a fluid pressure of 1 BAR: P = t x rpm x 2 x pi

## The Attempt at a Solution

Moment of inertia of the flywheel:

I = 0,5 x m x r

I = moment of inertia measured in kg m^2

0,5 = constant

m = total mass of the flywheel measured in kg

r = radius of the solid cylinder measured in meters

That gives:

I = 0,5 x 5 x 0,05 = 0,125 kg m^2

Angular velocity of the flywheel:

2pi x (RPM/60)

That gives:

1: (6,28 * (1050 / 60) = 109,9 radians/sec

2: (6,28 * (1100 / 60) = 115,1 radians/sec

3: (6,28 * (1150 / 60) = 120,4 radians/sec

Angular acceleration of the flywheel:

deltasomethingvalue/time = rad/s^2

(115,1 - 109,9) / 0,5 sec = 10,4 rad/s^2

Torque of the turbine:

moment of inertia x angular acceleration = torque

That gives us a average torque between 1050 RPM - 1100 RPM as following:

0,125 x 10,4 rad/s^2 = 1,3 Nm

Average power output of the turbine between 1050 RPM and 1100 RPM with a fluid pressure of 1 BAR:

P = t x rpm x 2 x pi = 1,3 x 1075 x 2 x 3,14

**= 146,2 watt**

I'm I right? I'm worried over the fact that I don't consider the width/height of the flywheel in my calculations for example. Note that english is not my native language and neither have I worked on above formulas before.

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