Centrifugal compressor slip factor: The slip factor is defined as the ratio of which velocity component to the blade tip speed (u2) at the impeller exit?
Correct Answer: Outlet whirl velocity to blade velocity
Introduction / Context:Due to finite blade number and flow separation, the actual tangential (whirl) component of absolute velocity at a centrifugal impeller exit is less than the ideal value. The slip factor quantifies this deficit and directly affects the achievable head rise from Euler’s equation.
Given Data / Assumptions:
- Steady operation at the impeller exit plane.
- Blade tip speed u2 is known from rotor speed and radius.
- Whirl (tangential) component at outlet is Vw2 (actual).
Concept / Approach:
A common practical definition is σ = Vw2(actual) / u2 when referenced to blade speed, representing the fraction of ideal whirl achieved. More rigorously, some texts define σ = Vw2(actual) / Vw2(ideal). Both convey that finite blades cause “slip,” reducing tangential momentum transfer and head rise.
Step-by-Step Solution:
Identify relevant velocity: tangential (whirl) at outlet, Vw2.Relate to blade tip speed u2 → σ ≈ Vw2 / u2 (in this option set).Select the option stating “outlet whirl velocity to blade velocity”.Conclude that slip lowers Euler head from the ideal prediction.Verification / Alternative check:
Performance correlations employ σ to correct the ideal head: Δh_actual ≈ σ * u2 * Vw2(ideal) / g, consistent with reduced Vw2.
Why Other Options Are Wrong:
Inlet quantities do not define exit slip. Flow (meridional) velocities govern continuity and diffusion but not the slip factor definition relative to whirl delivery.
Common Pitfalls:
Confusing slip factor with work or loading factor; mixing up whirl and meridional components; forgetting finite blade-number effects.
Final Answer:
Outlet whirl velocity to blade velocity