This sectioned lift-and-force pump uses a solid piston, a foot valve at the inlet and a separate delivery check valve. The two valves alternate so the return stroke fills the cylinder and the working stroke forces water toward the delivery line.
Lift and Force Pump Interactive Calculator
Estimate ideal displacement-based delivery, static-head pressure, hydraulic output and the corresponding ideal piston force. The result is a first-order water calculation, not a pump or structure rating.
Equation Used
- Water density is 1000 kg/m3 and g is 9.81 m/s2.
- Delivery head is static water head and excludes pipe and valve losses.
- The piston is solid and the inlet and delivery checks alternate ideally.
Bore, stroke and cycle rate determine swept delivery. The static-head calculation estimates water pressure, hydraulic power and ideal piston force; the diagram shows the alternating inlet and delivery checks.
Two alternating check valves
On the piston upstroke, pressure in the cylinder falls: the foot valve opens, the delivery valve closes and water enters below the solid piston. On the downstroke, the foot valve closes and the delivery valve opens, so the piston forces that trapped water into the delivery passage.
The animation identifies both valve states and is schematic. It does not infer valve timing, air-vessel dimensions or component proportions from the historical engraving.
Moving water against a delivery head
A force pump directs displaced water into a delivery pipe through a check valve. The solid-piston arrangement shown here fills on the upstroke and delivers on the downstroke.
Use the calculator to compare bore, stroke and cycle rate for a stated water head. Choosing an actual pump also requires its pressure rating, inlet conditions, drive arrangement and allowable operating speed.
Displacement and static-head model
For water at static head H, p = rho gH. Hydraulic output is pQ, and the ideal pressure force on the piston is p(pi D^2/4). The model omits dynamic and mechanical losses.
Worked example: 100 mm bore and 200 mm stroke
Take a 100 mm bore, 200 mm stroke, 40 complete cycles per minute, volumetric efficiency of 85% and static water head of 24 m. These are example inputs, not an operator capability or equipment rating.
The piston area is π(0.100)²/4 = 0.007854 m². Swept volume is 0.007854 × 0.200 = 0.001571 m³, or 1.571 litres per cycle.
Estimated delivery is 1.571 × 40 × 0.85 = 53.4 L/min. Static pressure is 1000 × 9.81 × 24 = 235,440 Pa, or 235.44 kPa. Ideal pressure force on the piston is approximately 1,849 N, and hydraulic output is approximately 209.6 W.
At the same assumed efficiency, 20 cycles/min gives 26.7 L/min and 60 cycles/min gives 80.1 L/min. Actual efficiency can change with speed and operating conditions. This calculation does not establish sustainable hand effort or the pump’s maximum speed.
What changes when you increase delivery?
| Change | Effect in this model | What still needs checking |
|---|---|---|
| Larger bore | Flow and ideal piston force both increase with bore diameter squared. | Rod, drive, barrel and valve loads. |
| Longer stroke | More volume is displaced each cycle. | Available travel, linkage geometry and acceleration loads. |
| Higher cycle rate | Calculated flow rises in proportion at fixed volumetric efficiency. | Valve response, inlet pressure and actual efficiency at that speed. |
| Greater static head | Pressure, piston force and hydraulic power rise. | Pressure rating and pipe and valve losses beyond static head. |
These comparisons do not specify maintenance intervals, dry-running tolerance, service life or purchase cost. Those depend on the particular pump and installation.
Lift-and-force pump questions
Does the piston-force result equal hand force?
No. It is the ideal pressure force on the piston. Hand force also depends on lever geometry, moving-part weight and friction.
How does changing bore affect the result?
At fixed stroke, cycle rate, efficiency and head, both flow and ideal piston force scale with bore diameter squared. A larger bore increases the drive load as well as the estimated delivery.
Does this predict priming or diagnose falling flow?
No. The calculation does not model air leakage, inlet conditions or changing valve and seal behavior. A measured-flow shortfall needs investigation using the particular pump’s service information.
Does the animation model an air vessel?
No. It shows the cylinder and alternating inlet and delivery checks. Air-vessel pressure fluctuations and flow smoothing are outside the calculation.
Does increasing cycle rate always increase actual delivery proportionally?
Only if volumetric efficiency stays unchanged. The calculator uses the efficiency you enter; it does not predict valve response or efficiency changes at higher speed.
Can this choose a motor or specify a pump conversion?
No. Hydraulic output is power delivered to the water under the entered assumptions. Drive selection also requires mechanical losses, starting and cyclic loads, the pump rating and its approved drive arrangement.
Does the head input determine maximum suction lift?
No. It sets the static-head pressure calculation. Suction performance depends on inlet pressure, water temperature, elevation, pipe losses and pump behavior; it is not derived from the volumetric-efficiency input.
Mechanism reference
- FAO, Water Lifting Devices: describes the force-pump solid piston, foot valve and delivery valve, and gives the standard piston-pump discharge relationship.
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