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Calculating the mechanical energy of a turbine

Calculations

Since the turbine is basically a spinning disc, we will need to examine the field of rotational mechanics. That is the mechanics of circular motion.

To calculate the kinetic energy of a spinning turbine we will use following formula:

Kinetic energy
= 1/2 x moment of inertia x angular velocity squared i.e.

KE = ? I ² measured in Joules

Moment of inertia of a turbine blade
= 1/2 x mass of the blade x radius squared i.e.

I = ?MR ² measured in kg.m ²

Angular velocity
= (2 x ) / period of revolution i.e.

measured in radians per second (rad s ^-1 )

For simplicity, suppose that a steam turbine has only one fan of mass 500kg with a radius of 2.0 m revolving at 6000 rpm (revolutions per minute). We now have enough information to calculate its kinetic energy.

Step 1. Calculate angular velocity.

= 628.3 rad s ^-1

Step 2. Calculate moment of inertia.

I = 1/2 MR ² = 1/2 x 500 x 2 ² = 1000.0 kg.m ²

Step 3. Calculate kinetic energy.

Substituting the results from step 1 and 2 into the following:

KE = 1/2 I ² = 1/2 x 1000.0 x 628.3 ²
= 197380445 Joules or 1.974 x 10 ⁸ Joules