Why are low pressure turbine blades larger

Why low pressure turbines have larger blades?

Low Pressure (LP) turbine blades have longer length so that:
- more force can be extracted --> FORCE = PRESSURE * AREA of blades
- the steam pressure has been reduced after coming from the high pressure (HP) turbine, therefore, to extract more force, the blade area of the low pressure turbine has to be larger
- the more force, the more work
- the more work, the more power output

Why are high pressure turbine blades smaller?

HP turbine have shorter blade length because:
- ANGULAR VELOCITY inversely proportional to RADIUS
- the smaller the turbine blade diameter, the faster it rotates
- the smaller the blades, the faster it turns
- smaller blades can withstand the higher pressure and higher velocity of steam
- smaller blade lengths are more robust against torsional failure and vibrations
- smaller blades can maintain the higher velocity of the steam

FORCE = MASS * ACCELERATION

FORCE = MASS * VELOCITY / TIME

- higher velocity means higher impulse
- higher impulse means higher force
- higher force means higher work done
- higher work means higher energy transferred to the shaft
- higher energy extracted means higher power output
- higher power output means higher thermal efficiency
- higher thermal efficiency means higher savings
- higher savings means higher benefits