Application of Euler’s turbomachinery equation: Euler’s head/energy equation is directly applicable to which of the following machines?

Introduction / Context:
Euler’s turbomachinery equation relates the change in angular momentum of a fluid to the shaft work exchanged in rotating machines. It underpins performance analysis for pumps, compressors, and turbines of various flow geometries.

Given Data / Assumptions:

• Steady, one-dimensional flow at rotor inlet and exit.
• Neglecting losses to state the ideal relation.
• Applies to rotating blades/impellers where whirl components exist.

Concept / Approach:

The equation states: specific work = u2 * Vw2 − u1 * Vw1, where u is blade speed and Vw is the whirl (tangential) velocity component. This is valid for any turbomachine—compressor or pump, radial or axial—so long as rotor-relative momentum exchange occurs.

Step-by-Step Solution:

Verification / Alternative check:

Derivations for compressor head rise and pump head both start from the same Euler relation, confirming universality across rotodynamic machines.

Why Other Options Are Wrong:

Restricting to only one type ignores the generality of the angular momentum principle. Reciprocating compressors are not turbomachines and are outside this framework.

Common Pitfalls:

Thinking the equation is exclusive to pumps or to compressors; overlooking that axial machines also have whirl at rotor inlet/outlet.

Final Answer:

All of these