Four-stage compressor with equal pressure ratio per stage: determine fourth-stage delivery pressure In a four-stage compressor operating with equal pressure ratio per stage, the pressures at the first and third stage are given as 1 bar and 16 bar, respectively. Assuming standard textbook staging with equal ratios, compute the delivery pressure at the fourth stage and choose the closest option.

Given data

• Number of stages = 4; equal pressure ratio per stage.
• Stated pressures: first stage = 1 bar; third stage = 16 bar.

Concept/ApproachFor equal pressure ratio r per stage, overall pressure after n stages is p_out = p_in × rⁿ. Standard MCQ convention often uses the given intermediate pressure (16 bar) as the pressure after the second stage, leading to a clean power-of-four result.

Step-by-step calculation (assumption noted)Assumption: The 16 bar value corresponds to the end of the second stage (a common textbook variant); then r² = 16 ⇒ r = 4.After four stages: p₄ = 1 × r⁴ = 4⁴ = 256 bar.

Verification/AlternativeIf 16 bar were strictly after the third stage with equal r, r³ = 16 ⇒ r ≈ 2.52 and p₄ ≈ 40 bar, which does not match the provided options. Hence the usual intended reading yields 256 bar.

Final Answer256 bar