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FLOW THROUGH A SINGLE STAGE

Objectives:

Obtain expressions for

1. Torque and work per stage
2. Stagnation temperature rise
3. Stagnation pressure rise
4. Stage efficiency
5. Limiting pressure ratio per stage,

and relate these to the stage velocity diagrams.

Reference Frames:

The velocity of air at any station, measured with respect to the engine walls, is called the "absolute velocity", denoted by .
The velocity of air measured relative to a rotor blade is .

Thus,

where the blade speed at that radius is

and

with N being the shaft speed in revolutions per minute (RPM).

Velocity Diagrams for a Single Stage

Conservation of Angular Momentum gives:
Torque per unit mass flow rate = rate of change of angular momentum

Assuming that radial movement of the air is negligible within each stage. Thus, air entering the stage at radius r will leave at the same radius r.


Work done on the fluid per unit time per unit mass flow rate by the rotor is:

Torque on the stator =

Work done by the stator is zero, because the stator blades do not move with respect to the engine walls.  Thus, there is no rise in stagnation enthalpy in the stator.

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