This page models only the ideal static force balance of a large water-driven piston rigidly coupled to a smaller output plunger. The piston-area ratio can multiply pressure, while real delivery head and flow depend on losses, valves, cycling and the complete machine.
Tramp Pumping Device Interactive Calculator
Enter a drive-piston bore, output-plunger bore and water supply head. Results are ideal static equivalents, not achievable pump ratings.
Equation Used
- Both entered bores define circular effective piston areas.
- The large drive piston and small output plunger are rigidly coupled and in static force balance.
- Supply head is converted to gauge pressure with water density 1000 kg/m^3 and standard gravity 9.80665 m/s^2.
- The displayed output head and pressure are ideal equivalents before all losses.
- Flow, stroke, cycle timing, valve behavior, friction, leakage, acceleration, power, efficiency, strength and safe design are omitted.
Large Drive Piston and Small Output Plunger
A hydraulic pressure intensifier can use a differential piston with a larger face exposed to supply pressure and a smaller opposite face generating higher pressure. Patent literature describes the ratio of those faces as the basic amplification factor.
This calculator represents only that ideal static balance. It does not model the valves, return stroke or reciprocating sequence required for a working pump.
What This Calculator Does
The tool converts entered water supply head to ideal gauge pressure, applies it to a circular drive-piston area, and balances that force against a smaller circular output-plunger area. It reports the piston-area ratio, ideal output-head equivalent, ideal gauge-pressure equivalent and ideal drive force.
It does not predict delivered flow, achievable lift, cycle rate, efficiency or machine capacity.
Ideal Static Intensifier Balance
ps = rho g Hs
FD = psAD
po = ps(AD/Ad)
Ho = Hs(AD/Ad)
The displayed pressure is gauge pressure for the stated ideal water-column assumption. Standard gravity is 9.80665 m/s^2 and rho is fixed at 1000 kg/m^3.
Worked Ideal Example
For D=200 mm, d=40 mm and Hs=8 m, the piston-area ratio is 25:1. The ideal balance head is 200 m, the ideal gauge-pressure equivalent is about 1961 kPa and the ideal supply-head force on the drive piston is about 2.46 kN.
Those are static lossless equivalents, not a promise of delivered head or flow.
Model Boundary
- Mechanical arrangement: a differential piston uses a larger supply-pressure face and a smaller high-pressure face; their area ratio sets ideal pressure amplification.
- Calculated: circular areas, water-head pressure and lossless static force balance.
- Not calculated: rod or annular areas, valve topology, check-valve cracking pressure, suction, priming, return stroke, self-cycling, stroke volume, flow, speed, acceleration, water hammer, cavitation, friction, seal drag, leakage, compressibility, accumulator behavior, efficiency, power, heat, stress, fatigue, materials, corrosion, pressure containment, relief protection or safe design.
Frequently Asked Questions
Is ideal balance head the height the pump will reach?
No. It is the static lossless pressure equivalent. A real machine must retain margin for flow and all losses.
Does a diameter ratio equal the pressure ratio?
No. For circular pistons, the ideal pressure ratio is the square of the bore-diameter ratio.
Does the calculator predict flow?
No. Stroke, cycle rate, valve timing and volumetric losses are absent.
Does the animation prove the device will self-cycle?
No. It is only a kinematic illustration of coupled piston motion.
Is water density always exactly 1000 kg/m^3?
No. That is the stated calculation convention; actual density varies with temperature and composition.
Can these results size a pressure vessel or pump?
No. Pressure containment and machine design require complete engineering analysis and applicable requirements.
References
- U.S. Patent 9,562,544, Hydraulic system: differential piston with a larger supply-pressure face and smaller high-pressure face, with face-area ratio determining the basic amplification factor.
- U.S. Patent 6,086,338, Water jet intensifier pump having a piston arrangement with a ceramic liner: fluid-driven piston and coupled plunger compressing fluid in a high-pressure chamber.
- U.S. Geological Survey, Basic Ground-Water Hydrology: hydrostatic relation p=rho g h and pressure-head definition.
- NIST SP 811, Appendix B.9: standard acceleration of free fall 9.80665 m/s^2.
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