Cylinder sizing in compound engines: In a compound steam engine the first stage of expansion occurs in the high-pressure (H.P.) cylinder and the final expansion in the low-pressure (L.P.) cylinder. The diameter of the H.P. cylinder is __________ the diameter of the L.P. cylinder.

Introduction / Context:
Compound engines divide expansion between cylinders operating at different pressures. The cylinder sizes are chosen so that each stage contributes appropriately to the total work with reasonable steam velocities and mechanical stresses.

Given Data / Assumptions:

• H.P. cylinder handles high inlet pressure and small specific volume.
• L.P. cylinder handles lower pressure and larger specific volume after partial expansion.
• Similar piston speeds are desirable across stages.

Concept / Approach:
Because steam specific volume increases as pressure falls during expansion, the L.P. cylinder must have a larger volume (and hence larger diameter for similar stroke) to pass the increased volumetric flow. Therefore, the H.P. cylinder diameter is less than that of the L.P. cylinder. This sizing keeps velocities and pressure drops within acceptable limits and balances indicated power between cylinders.

Step-by-Step Solution:
Relate specific volumes: v_LP > v_HP for the same mass flow.To accommodate higher volumetric flow at low pressure, cylinder area must be larger.For equal strokes, larger area implies larger diameter for L.P. cylinder.Hence, D_HP < D_LP → “less than”.

Verification / Alternative check:
Design examples and textbooks show L.P. cylinder diameter commonly 1.5–2 times the H.P. cylinder diameter depending on pressure ratios and receiver effects.

Why Other Options Are Wrong:
Equal/more than/double: contradict basic volumetric reasoning unless strokes differ greatly; typical practice uses larger L.P. diameter.

Indeterminate: although exact ratio needs data, the directional relation is well established.

Common Pitfalls:
Assuming equal diameters or ignoring volumetric flow increase during expansion.

Final Answer:
less than