Two-stage reciprocating air compressor with complete intercooling: diameter ratio relation Let p₁ be the suction pressure to the L.P. cylinder and p₂ the pressure leaving the L.P. cylinder (intercooler pressure). For a single-acting, two-stage reciprocating air compressor with complete intercooling, what is the correct relation for the cylinder diameter ratio D₁/D₂? Choose the correct option.

Given data

• Single-acting, two-stage reciprocating air compressor.
• Complete intercooling (air cooled back to initial suction temperature between stages).
• D₁ = diameter of L.P. cylinder; D₂ = diameter of H.P. cylinder; p₁ = suction pressure to L.P.; p₂ = delivery pressure from L.P. (and intercooler pressure).

Concept/ApproachWith complete intercooling to the initial temperature, the specific volume at each stage inlet is inversely proportional to the stage inlet pressure. For equal piston speeds, volumetric flow rate ∝ cylinder area, so the area (and hence diameter) ratio follows the square root of the pressure ratio seen across the stages.

Key relationA₁/A₂ = V̇₁/V̇₂ = (p₂/p₁) ⇒ (D₁/D₂)² = p₂/p₁ ⇒ D₁/D₂ = √(p₂/p₁).

Why given options are incorrectOptions (a), (b), and (c) omit the required square root; therefore the correct choice is None of these.

Final AnswerNone of these (correct relation is D₁/D₂ = √(p₂/p₁)).