Question

Which of the following statements is/are TRUE for an axial turbine?

• A. For a fixed rotational speed, the mass flow rate increases with increase in the flow coefficient
• B. The absolute stagnation enthalpy of the flow decreases across the nozzle row
• C. The relative stagnation enthalpy remains unchanged through the rotor
• D. For a fixed rotational speed, the mass flow rate remains unchanged with a change in the flow coefficient

Hint:

Stator: \(h_0\) constant, \(p_0\downarrow\). Rotor: conserve rothalpy, not \(h_{0,\text{rel}}\). Flow coefficient \(\phi\) scales \(V_x\Rightarrow \dot m\propto \phi\) at fixed speed.

Answer 1

The Correct Option is A

Step 1: Flow coefficient and mass flow (fixed speed).
Flow coefficient \(\phi = V_x/U\) (axial velocity over blade speed). With rotational speed fixed \(\Rightarrow U=\) const; increasing \(\phi\) increases \(V_x\) and therefore \(\dot m=\rho A V_x\) (for given \(\rho,A\)) increases. \(\Rightarrow\) (A) True; (D) contradicts this and is False.
Step 2: Stator (nozzle) total enthalpy.
Across an adiabatic stator (no shaft work), the absolute stagnation enthalpy \(h_0\) (and \(T_0\)) remain essentially constant; only \(p_0\) drops as kinetic energy rises. \(\Rightarrow\) (B) False.
Step 3: Rotor and relative stagnation enthalpy.
In a rotor there is work exchange; the conserved quantity (adiabatic, steady, inviscid) is the rothalpy, not the relative stagnation enthalpy \(h_{0,\text{rel}}=h+\tfrac{W^2}{2}\). Thus \(h_{0,\text{rel}}\) generally changes through the rotor. \(\Rightarrow\) (C) False.
\[ \boxed{\text{Only (A) is correct.}} \]