Formula:
The discharge of a double-acting reciprocating pump is given by:
Q = (L x A x N)/60

Explanation:
To understand the given formula, let's break it down into its components:

- L: length of stroke, which is the distance travelled by the piston from one end to the other end of the cylinder.
- A: cross-sectional area of the piston, which is the area of the circular piston face.
- N: speed of crank in RPM, which is the number of revolutions per minute.

The formula calculates the discharge of the pump, which is the volume of liquid delivered by the pump per unit time. The units of discharge are usually liters per minute (LPM) or cubic meters per hour (m3/h).

Now, let's see how the formula is derived:

- The piston of the double-acting reciprocating pump moves back and forth inside the cylinder, creating a suction and discharge cycle.
- During one complete cycle, the piston moves from one end of the cylinder to the other end and back.
- The volume of liquid displaced by the piston during one stroke is equal to the cross-sectional area of the piston (A) times the length of stroke (L).
- The pump makes N revolutions per minute, so the number of strokes per minute is also N.
- Therefore, the total volume of liquid displaced by the pump per minute is N times the volume of liquid displaced by the piston per stroke, which is (L x A).
- Finally, to convert the volume per minute into volume per second, we divide by 60, which gives us the formula:

Q = (L x A x N)/60

Conclusion:
The correct answer is option D, i.e., 2LAN/60. This is because the formula for discharge of a double-acting reciprocating pump is (L x A x N)/60, and the question asks for the discharge in liters per second, which requires dividing the result by 60. Additionally, since the pump is double-acting, the volume of liquid displaced per stroke is twice the volume of the single-acting pump, so we need to multiply the formula by 2. Hence, the final formula is 2(L x A x N)/60, which simplifies to 2LAN/60.