Parsons (50% reaction) stage geometry:\nFor a pure Parsons reaction turbine stage, if α1 and α2 are the fixed (stator) blade inlet and exit angles, and β1 and β2 are the moving (rotor) blade inlet and exit angles, identify the correct angular relationships.

Introduction / Context:
Parsons turbines are designed for 50% degree of reaction with symmetrical velocity triangles. Recognizing the symmetry between stator and rotor flow angles is vital for quick sketches of velocity diagrams and for understanding how reaction is shared between fixed and moving rows.

Given Data / Assumptions:

• Idealized 50% reaction stage (Parsons stage).
• Negligible profile and leakage losses for geometric relations.
• Axial velocity approximately constant across the stage.

Concept / Approach:
In a Parsons stage, the velocity triangles are geometrically similar and mirror each other about the axial direction. This leads to equality of corresponding angles: the stator exit angle equals the rotor inlet angle, and the stator inlet angle equals the rotor exit angle. Hence α1 (stator inlet) = β2 (rotor exit) and α2 (stator exit) = β1 (rotor inlet). This symmetry underpins the 50% reaction distribution between stator and rotor.

Step-by-Step Solution:

Verification / Alternative check:
Textbook Parsons stage diagrams confirm mirrored triangles about the axial line, giving the same equal-angle relations stated above.

Why Other Options Are Wrong:

• α1 = α2 and β1 = β2: Implies no flow turning in rows, which is incorrect.
• α1 = β1 and α2 = β2: Confuses inlet/exit pairings; these are generally not equal.
• α1 < β1 and α2 > β2: No general rule of this type applies for a pure Parsons stage.

Common Pitfalls:
Mixing absolute (α) and relative (β) angle definitions; ensure α refers to absolute flow angles at stator, β to relative flow angles at rotor.

Final Answer:
α1 = β2 and β1 = α2