A double-acting force pump uses two suction checks and two delivery checks to pump on both directions of piston travel. While one chamber fills, the other expels liquid. A rod on one side reduces that side’s swept volume, so the two deliveries generally differ.
Double-acting Force Pump Interactive Calculator
Size the geometric delivery of a four-check-valve double-acting pump. The cutaway follows the piston, rod-side volume and the two alternating valve pairs. The flow graph shows why delivery on both strokes still pulsates.
Equation Used
- One complete reciprocating cycle per entered cycle count.
- Rod is present on the right side only, with 0≤d<D.
- Ideal incompressible swept volume and instantaneous check-valve response.
- The efficiency input adjusts mean flow without predicting the cause of losses.
- Sinusoidal motion is prescribed; a particular crank and connecting rod are not modeled.
Efficiency is an entered assumption, not a predicted pump performance or guaranteed actual flow. A rod equal to or larger than the bore is flagged as invalid geometry. At zero speed, displacement per cycle remains defined but delivery per minute is zero.
Follow the open pair of valves
The cutaway places the delivery header above the cylinder and the suction header below it. Each chamber connects to one suction valve and one delivery valve.
As the piston moves right, the left suction valve opens and the right delivery valve opens. The left delivery and right suction valves stay closed. On the return movement, the opposite pair opens. All four checks are drawn seated at the ideal reversal instant.
The piston rod leaves through the right end cover. Its diameter is drawn relative to the bore and reduces the working area of the right chamber. The rod moves with the piston and retains a fixed drawn length.
Hiscox’s mechanism 511 illustrates the same double-acting lift-and-force principle in a vertical arrangement. The horizontal cutaway separates the four flow branches and includes rod area in the displacement calculation.
Estimate displacement and mean delivery
The calculator is useful for comparing bore, rod diameter, stroke and cycle rate. It calculates displaced volume, then uses the entered efficiency as an allowance for the difference between theoretical and estimated delivered flow.
It does not establish a pressure rating, motor power, maximum suction lift or suitability for a particular liquid. Those questions require the actual pump construction and operating conditions.
Two swept areas
The cap-side area is A=πD²/4. The rod-side area is A−a, where a=πd²/4. A complete cycle therefore delivers AS+(A−a)S=(2A−a)S in the ideal volume model.
With dimensions in millimetres, divide cubic millimetres by 1,000,000 to obtain litres. Multiplying litres per cycle by complete cycles per minute gives mean litres per minute. The efficiency-adjusted estimate uses ηv/100 as a multiplier.
The displacement reduction relative to a rodless double-acting cylinder is aS/(2AS)=a/(2A). It is a geometric difference, not a leakage or energy loss.
For the displayed sinusoidal motion, piston speed magnitude is πSN|sin(2πp)| in mm/min, where p is cycle fraction. Multiplication by the active delivery area gives the instantaneous theoretical flow. It reaches zero at both reversals.
100 mm bore, 40 mm rod
At a 150 mm stroke, the 100 mm bore gives 1.178 L on the cap-side delivery and the 40 mm rod reduces the other delivery to 0.990 L. Total ideal displacement is approximately 2.168 L per cycle.
At 60 complete cycles per minute, mean theoretical flow is approximately 130.1 L/min. A supplied 90% volumetric efficiency gives an estimated 117.1 L/min. The rod accounts for an 8% reduction from a hypothetical rodless double-acting cylinder.
Doubling cycle rate doubles both flow outputs without changing litres per cycle. Setting speed to zero stops the animation and gives zero flow per minute while retaining the geometric displacement.
Double acting still means pulsating
The graph displays the two unequal flow lobes and their zero-flow reversals. The dashed line is the mean theoretical flow; it is not the instantaneous flow at every piston position. An accumulator or multiple cylinders could change the delivery waveform, but neither is simulated here.
Valve motion and the fluid arrows identify the connected flow route. They do not predict pressure drops, valve inertia, leakage, compressibility or liquid particle trajectories. Bore and rod share a radial scale; stroke has its own display scale.
Force pump questions
Why are the two flow peaks different?
The right chamber contains the rod and has less working area.
Why does changing efficiency not change the valves?
Efficiency adjusts estimated mean delivery. It does not define a different valve sequence.
Is speed the number of individual strokes?
No. It is the number of complete out-and-back cycles per minute.
Why does zero rod diameter still show a drive connection?
The zero value is a rod-area-neglected limit; a thin dashed centreline indicates the idealized external drive.
Is the displayed flow guaranteed?
No. The theoretical flow is swept-volume arithmetic; the efficiency-adjusted flow uses your supplied assumption.
Reference
Hiscox, Mechanical Movements, Powers, Devices and Appliances, mechanism 511, printed page 140 (PDF page 150): double-acting lift-and-force pump with alternating suction and delivery checks.
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