Question

The discharge through a single acting reciprocating pump is

• A. $Q = \frac{ALN}{60}$
• B. $Q = \frac{LN}{60A}$
• C. $Q = 2ALN$
• D. $Q = \frac{ALN}{3600}$

Hint:

For a single-acting pump, the volume discharged per revolution is $A \cdot L$. Dividing by 60 converts the rotational speed $N$ from RPM to RPS, yielding $Q = \frac{ALN}{60}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A reciprocating pump is a positive displacement pump that uses a piston or plunger moving back and forth inside a cylinder to pump fluid.
A single-acting pump discharges fluid only during one forward stroke of the piston, while the return stroke draws fluid into the cylinder.

Step 2: Detailed Explanation:
To calculate the theoretical discharge ($Q$) of a single-acting reciprocating pump:
The volume of water displaced during a single stroke of the piston is equal to the cross-sectional area of the piston ($A$) multiplied by the stroke length ($L$):
\[ \text{Volume per stroke} = A \cdot L \]
Since fluid is discharged only once per complete revolution of the drive shaft, the volume discharged per revolution is also $A \cdot L$.
If the pump shaft rotates at a speed of $N$ revolutions per minute (RPM), the total volume discharged per minute is:
\[ \text{Volume per minute} = A \cdot L \cdot N \]
To convert this flow rate to standard units of volume per second (m$^3$/s), we divide the volume per minute by 60 seconds:
\[ Q = \frac{A \cdot L \cdot N}{60} \]
For a double-acting reciprocating pump, fluid is discharged during both strokes, so the discharge is doubled:
\[ Q_{\text{double}} = \frac{2 \cdot A \cdot L \cdot N}{60} \]
Therefore, the correct equation for a single-acting pump is $Q = \frac{ALN}{60}$.

Step 3: Final Answer
The theoretical discharge through a single-acting reciprocating pump is given by the equation $Q = \frac{ALN}{60}$.