Throttle-Governed Steam Engine — Interpolating Steam Rate vs. Power A throttle-governed steam engine develops 15 kW using 280 kg/h of steam and 35 kW using 520 kg/h of steam. Assuming linear variation of steam consumption with power over this range, estimate the steam consumption (kg/h) when the engine develops 20 kW.

Introduction / Context:In practical testing of small throttle-governed steam engines, the total steam consumption S (kg/h) commonly follows an approximately linear relationship with brake power P (kW) over a modest operating band. This is because throttling and part-load losses vary gradually, while mechanical losses are relatively stable. Interpolation between two measured points is therefore a standard engineering technique to estimate consumption at an intermediate power.

Given Data / Assumptions:

• At P1 = 15 kW, steam rate S1 = 280 kg/h.
• At P2 = 35 kW, steam rate S2 = 520 kg/h.
• Throttle-governed engine; assume S varies linearly with P between these two points.
• We require S when P = 20 kW.

Concept / Approach:Use straight-line interpolation. If S varies linearly with P, then the slope m = (S2 − S1) / (P2 − P1). Once m is known, the steam rate at any intermediate power P is S = S1 + m * (P − P1). This is equivalent to constructing the equation of a line through two points and evaluating it at the desired P. This approach is widely applied when only limited test points are available and the operating interval is small.

Step-by-Step Solution:Compute slope: m = (520 − 280) / (35 − 15) = 240 / 20 = 12 kg/h per kW.Target power: P = 20 kW, difference from P1: ΔP = 20 − 15 = 5 kW.Interpolate: S = S1 + m * ΔP = 280 + 12 * 5 = 280 + 60 = 340 kg/h.Therefore, the estimated steam consumption at 20 kW is 340 kg/h.

Verification / Alternative check:Check reasonableness by computing specific steam consumption. At 15 kW: 280 / 15 ≈ 18.7 kg/kWh; at 35 kW: 520 / 35 ≈ 14.9 kg/kWh; at 20 kW (estimated): 340 / 20 = 17.0 kg/kWh, which falls sensibly between the two measured values—consistent with improved efficiency at higher load.

Why Other Options Are Wrong:

• 150 kg/h or 210 kg/h: imply unrealistically low specific steam consumption relative to measured data.
• 280 kg/h: equals the 15 kW datum; ignores increased power.

Common Pitfalls:Assuming proportionality between S and P through the origin. Real engines have load-independent losses; hence the line does not pass through zero. Interpolation between actual data points avoids this mistake.

Final Answer:340 kg/h