Impulse turbine kinematics — finding the nozzle (inlet) steam velocity A single-stage impulse turbine has a rotor mean diameter of 1.2 m and runs at 3000 r.p.m. The blade speed ratio (φ = U / V1) is 0.42, where U is the blade peripheral (tip) speed and V1 is the absolute inlet steam velocity from the nozzle. Determine the inlet steam velocity V1.

Introduction / Context:
Velocity triangles in impulse turbines relate blade speed to the absolute jet velocity issued by the nozzle. The blade speed ratio φ = U/V1 is a convenient non-dimensional parameter used for design and performance matching of a single stage.

Given Data / Assumptions:

• Mean rotor diameter D = 1.2 m.
• Rotational speed N = 3000 r.p.m.
• Blade speed ratio φ = 0.42, with φ = U / V1.

Concept / Approach:
First compute the blade peripheral speed U from rotational kinematics, then invert the blade speed ratio to find V1. The relation for peripheral speed is U = π * D * N / 60. Finally, V1 = U / φ.

Step-by-Step Solution:
Compute U: U = π * 1.2 * 3000 / 60 = π * 1.2 * 50 = 60π ≈ 188.5 m/s.Use φ = U / V1 ⇒ V1 = U / φ.Substitute values: V1 ≈ 188.5 / 0.42 ≈ 449 m/s.Round sensibly for engineering reporting: V1 ≈ 450 m/s.

Verification / Alternative check:
The result is consistent with typical nozzle exit velocities for impulse stages operating near 3000 r.p.m. on a 50 Hz grid using D ≈ 1.2 m, where inlet velocities of several hundred m/s are common.

Why Other Options Are Wrong:
79 m/s and 188 m/s align with blade speeds, not jet speeds. 900 m/s is unrealistically high for the given φ and would require U ≈ 378 m/s, which contradicts the calculated U.

Common Pitfalls:
Confusing tip speed U with inlet steam velocity; misusing φ as V1/U instead of U/V1, which would invert the result.

Final Answer:
450 m/s