Sizing the Cylinder to the Well: A Force-Balance Rule for Hand-Pump Bore Diameter Against Depth

A hand pump asks one person to lift, on every upstroke, the entire column of water standing above its piston. That simple fact places a hard ceiling on how wide the cylinder bore may be for a given depth of water, yet bore diameters are commonly chosen from what is available, what a neighbouring installation uses, or what a supplier stocks, rather than from the force the operator can actually deliver. This paper derives a closed-form sizing rule from a force balance on the upstroke: the force available at the pump rod, given by a stated sustainable handle force multiplied by the lever ratio of the handle, must cover the weight of the water column on the piston, the weight of the pump rod, and seal friction. Solving that balance for bore diameter gives the largest bore an operator can work at each depth. Under the central assumptions — a sustainable handle force of 150 N, a lever ratio of 4, seal friction of 45 N, and a steel pump rod of 12 mm diameter weighing 8.709 N per metre — the maximum bore is 77.9 mm at a depth of 10 m, 49.7 mm at 20 m, 35.6 mm at 30 m, and 25.9 mm at 40 m. Read in the other direction, a bore of 50 mm reaches its limit at a depth of 19.8 m, a bore of 75 mm at 10.7 m, and a bore of 100 mm at 6.5 m. Rod weight, often ignored in informal sizing, is a first-order term: at a depth of 30 m the rod alone weighs 261.3 N, against 555 N available at the rod after seal friction in the central case. The rule is presented with sensitivity tables for lever ratio and handle force so that it can be applied with values appropriate to a particular pump and a particular operator.