Reciprocating Pump with Air Vessel — Percentage Saving in Work (Single-Acting) An air vessel is fitted to a single-acting reciprocating pump to smoothen flow and reduce acceleration head. The percentage saving in work (and thus power) due to the air vessel is approximately:

Introduction:
Reciprocating pumps experience periodic acceleration and deceleration of the liquid column in the suction and delivery pipes, creating acceleration head and extra work per cycle. Air vessels reduce this unsteadiness, cutting energy losses. This question asks for the approximate saving for a single-acting pump.

Given Data / Assumptions:

• Single-acting reciprocating pump with sinusoidal piston motion.
• Long pipes where acceleration head is significant.
• Air vessel properly located near cylinder on suction and/or delivery side.

Concept / Approach:
With an air vessel, the flow in the pipe becomes nearly uniform, and the fluctuating component of kinetic energy is largely eliminated. Classical analysis shows the reduction in work per cycle is about 39.2% for a single-acting pump (and about 48.8% for double-acting), assuming ideal placement and negligible secondary losses.

Step-by-Step Solution:
Without air vessel: periodic velocity in pipe causes added acceleration head h_as ∝ L * A_piston / (g * a_pipe) * r * ω^2 * cos(ωt), leading to extra work.With air vessel: the vessel supplies/absorbs flow during stroke reversals, flattening the pipe velocity waveform.Theoretical derivation yields percentage saving ≈ 39.2% for single-acting geometry and motion.

Verification / Alternative check:
Design texts cite ~39.2% for single-acting and ~48.8% for double-acting pumps; field results vary slightly depending on pipe inertia and vessel sizing.

Why Other Options Are Wrong:

• 48.8%: Corresponds to double-acting pumps, not single-acting.
• 84.8% and 88.4%: Unrealistically high; would imply near-total elimination of dynamic effects.

Common Pitfalls:
Confusing single- vs double-acting values or misplacing the air vessel too far from the cylinder, which reduces the actual benefit.

Final Answer:
39.2%