Hydraulic Ram Pump: Water-Hammer Pumping Cycle

Drive Conditions

Drive head H 1.5 m

Delivery lift h 8 m

Waste-valve trip speed 1.5 m/s

Drive pipe length L 6 m

Cycle State

Phase: accelerating
Pipe velocity: 0.00 m/s
Surge pressure: 0.0 m head

Cycle rate

-- /min

Delivered flow

-- L/min

Efficiency (D'Aubuisson η = qh / QH)

-- %

How it works

A hydraulic ram uses no motor — it pumps a small fraction of its own drive water uphill by repeatedly harnessing water hammer. Each cycle has three phases:

Accelerate — the waste valve is open, so water accelerates down the drive pipe under head H: dv/dt = gH/L − kv²/L (gravity vs. pipe friction).
Slam / surge — once v reaches the trip speed, the waste valve snaps shut. The abrupt deceleration launches a pressure wave described by the Joukowsky equation:

Δp = ρ·c·Δv   (surge head Δh = c·Δv / g)
c = pressure-wave speed in the pipe (~900–1400 m/s)
pulse duration ≈ 2L/c  (round-trip of the wave)

Deliver — if the surge head (H + Δh) exceeds the delivery lift h, the check valve opens for that pulse and pushes a slug of water into the air chamber, which cushions the shock and smooths the flow up the delivery pipe. The valve then reopens and the cycle repeats, typically 20–100 times per minute.

Only a fraction of the supplied water is delivered — the rest is the "waste" flow that powers the hammer. Efficiency is compared with two classic formulas:

D'Aubuisson: η = q·h / (Q·H)
Rankine:      η = q·(h−H) / ((Q−q)·H)

Real-world relevance: hydraulic rams have pumped water for farms and villages without electricity since the 1770s, and are still used today anywhere a stream with a modest fall needs to lift water higher than its own source — the same Joukowsky surge this simulator visualises is also what engineers must damp in long pressurised pipelines to avoid pipe-bursting transients.

Drive flow Delivered flow Waste discharge

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