Question

In a single acting reciprocating pump (hydraulic), work saved in friction due to fitting of air vessel is:

• A. 39.2 %
• B. 50.0 %
• C. 65.5 %
• D. 84.8 %

Hint:

To remember these percentages for exams: The "Single" pump is more inefficient on its own, so it has more to gain from an air vessel (84.8%). The "Double" pump is already smoother, so it saves less (39.2%).

Answer 1

The Correct Option is D

1. Function of an Air Vessel: An air vessel is a closed container, partially filled with the liquid being pumped and partially with compressed air. It acts as a reservoir that smooths out the pulsating flow from the reciprocating piston, converting it into a nearly uniform flow in the rest of the piping system.

2. Friction Loss Mechanism: Friction loss in a pipe is proportional to the square of the velocity ($V^2$).

• Without Air Vessel: The velocity varies sinusoidally, leading to high instantaneous velocities and very high friction losses.

• With Air Vessel: The velocity becomes uniform and much lower than the peak velocity of a pulsating flow, significantly reducing the friction head.

3. Mathematical Derivation of Work Saved: Through mathematical integration of the friction head over a complete cycle:

• For a

Single-Acting Pump, the theoretical work saved in overcoming friction is approximately