Gas Turbine Metrics — Definition of Work Ratio In a simple gas turbine (Brayton) plant, the work ratio is defined as which of the following expressions, where W_t is turbine work and W_c is compressor work?

Introduction / Context:
Besides thermal efficiency, gas-turbine designers track the work ratio to see how much of the turbine’s output is actually available as net work after driving the compressor. A higher work ratio indicates a larger fraction of the turbine work remains for useful output.

Given Data / Assumptions:

• Ideal Brayton components for definition; real losses are not needed to define the metric.
• Single-shaft or coupled turbine-compressor arrangement.
• W_t and W_c are per unit mass of working fluid.

Concept / Approach:
Net work W_net = W_t - W_c. Work ratio wr is defined as W_net divided by turbine work output: wr = (W_t - W_c) / W_t. This reveals how much of the turbine’s gross power escapes the internal demand of the compressor.

Step-by-Step Solution:
Define W_net = W_t - W_c.Define wr = W_net / W_t.Substitute W_net ⇒ wr = (W_t - W_c) / W_t.

Verification / Alternative check:
In practice, simple gas turbines often have wr in the 0.3–0.5 range at design point; improvements like intercooling/recuperation alter W_c and W_t, affecting wr accordingly.

Why Other Options Are Wrong:
(W_t - W_c)/W_c, W_t/W_c, and W_c/W_t describe other ratios (net-to-compressor, turbine-to-compressor, compressor-to-turbine) and are not the standard definition of work ratio.

Common Pitfalls:
Confusing work ratio with back work ratio (defined as W_c/W_t), which quantifies the compressor’s fraction of turbine work.

Final Answer:
(W_t - W_c) / W_t