For the selected ideal isothermal event, air begins at 14.7 psia in volume Vstart and ends at Vend. The maximum chamber gauge pressure is max[0, 14.7(Vstart/Vend − 1)]. Available load gauge after the selected outlet cracking differential is max(0, Pchamber − Pcrack).
Port-refilled Single-valve Air Pump
Check one selected ideal isothermal air-chamber event against an outlet cracking differential and load pressure.
Equation Used
- The chamber begins at 14.7 psia at the selected starting volume.
- Compression or expansion is treated as an ideal isothermal event.
- Outlet opening requires chamber gauge to exceed load gauge plus the selected cracking differential.
- Flow, valve dynamics, refill, leakage, forces, heat-transfer rate and ratings are excluded.
The wall ports refill the animated cylinder. The calculator below remains a separate sealed-event pressure comparison.
Wall-port refill and one delivery valve
Hiscox figure 653 uses perforations near the cylinder top for intake. Raising the piston uncovers them and admits air; lowering it closes them and compresses the trapped charge. The delivery check opens above the selected load plus cracking differential, then closes during the return stroke. The illustration holds pressure at that threshold during delivery and allows the remaining gas to expand on return. Instant refill, isothermal gas and negligible valve-flow resistance are idealizations; no flow rate is calculated.
What the calculator determines
Select starting and ending chamber volumes, load gauge pressure and outlet cracking differential. The calculator reports the selected volume ratio, ideal ending chamber gauge pressure, ideal available load gauge and any shortfall versus the selected load.
Ideal isothermal event
Pabs,end = 14.7(Vstart/Vend) psia; Pgauge,end = max[0, 14.7(Vstart/Vend − 1)]; Pavailable = max(0, Pgauge,end − Pcrack); shortfall = max(0, Pload − Pavailable).
Selected-input arithmetic
For 8 mL compressed to 2 mL, ideal ending chamber gauge pressure is 44.1 psi. With a 1 psi cracking differential, ideal available load gauge is 43.1 psi.
Event check only
The calculator treats the selected volumes as a sealed-gas event. The animation separately illustrates an ideal pumping cycle with instant refill and delivery at constant pressure. Connecting-passage volume, heat-transfer rate, valve dynamics, flow resistance, leakage, piston force, seal friction, efficiency and pressure ratings are not calculated.
Questions
Does this predict flow rate?
No.
What if ending volume is not smaller?
The selected event does not build positive gauge pressure in this reference, so the displayed maximum gauge is clamped to zero.
References & Further Reading
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), page 175, figure 653: single-valve air pump.
- Wikipedia contributors. Air pump. Wikipedia
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