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Hydraulic cylinder, 3.25 in bore and 1.375 in rod at 2,000 lb/in² and 10 gal/min: forces, speeds, cycle time, power and meter-out intensification

Tool	Hydraulic and Pneumatic Cylinders
Source	U.S. Army (1997). Hydraulics. FM 5-499, par. 1-1b and page 1-4 (F = PA), page 1-5 (Pascal's apparatus) and par. 6-4c, page 6-13 (HP = f p / 1,714); U.S. Navy (1990). Fluid Power. NAVEDTRA 12964, pages 2-6 to 2-9 (force, differential areas, volume and distance) and 2-15. The relations are the manuals'; the cylinder is illustrative.
Level	Undergraduate

Problem

A double-acting hydraulic cylinder with a 3.25 in bore, a 1.375 in rod and a 24 in stroke is supplied with 10 gal/min at 2,000 lb/in² (no back pressure; force efficiency 0.95, pump 0.85, motor 0.90). Find the extend, retract and regenerative forces and speeds, the cycle time, the bore a 12,000 lb load needs at a load factor of 0.8, the hydraulic power with the drive input, and the rod-end pressure when the extension is controlled by a meter-out flow control against a 5,000 lb load.

Inputs to Enter

Analysis: hydraulic force, speed and power; D 3.25 in, d 1.375 in, S 24 in, p 2,000 lb/in²
Q 10 gal/min, back pressure 0, force efficiency 0.95, pump efficiency 0.85, motor efficiency 0.90, load 12,000 lb, load factor 0.8, dwell 0 s, meter-out load 5,000 lb

Open the Hydraulic and Pneumatic Cylinders tool (loaded with this example)

Answers

Areas: cap end 8.296 in², rod end 6.811 in², rod 1.485 in²; area ratio 1.218
Forces: extend 15,762 lb (theoretical 16,592), retract 12,941 lb, regenerative extend 2,821 lb
Bore for the 12,000 lb load at LF 0.8: area 7.895 in², D 3.170 in, so the 3.25 in bore serves; it needs 1,523 lb/in² and the load is 0.761 of its extend force
Speeds: extend 23.20 ft/min (4.641 in/s, 5.171 s), retract 28.26 ft/min (4.246 s), regenerative 129.6 ft/min; cycle 9.417 s; 12.18 gal/min leaves the cap end while retracting
Power: p Q = 11.67 hp (10 × 2,000 / 1,714), pump shaft 13.73 hp, drive input 15.25 hp, rod power extending 11.08 hp, overall 0.727
Meter-out: rod-end pressure 2,436 lb/in² with no load (1.218 × supply) and 1,702 lb/in² against the 5,000 lb load

Notes

The tool's default inputs are this case; press Submit. The cylinder is illustrative (stated on the page), not a printed example: the force, power and gas-law examples the two manuals do print (5,000 lb, 500 lb, 120 / 80 / 40 lb, 1,250 lb, HP = f p / 1,714, Boyle's 61.77 lb/in² gauge) are reproduced in test_hydraulic_pneumatic_cylinders.php (1,098 checks) together with an independent numpy/scipy script. The other four analyses of the select (pneumatic, structural, dynamics, accumulator) have their own illustrative defaults.