The Pump That Throws Its Water Away

A hydraulic ram lifts water far higher than it fell, with no motor and no fuel: two valves, a pipe and a pulse. Run one here, the 2-inch ram that two Illinois engineers measured in 1941, simulated as a water-hammer wave in the pipe. Slow it down five hundred times and watch the delivery happen as a staircase of pressure waves, not the single blow the knocking suggests. Then the price: most of the water is thrown away, and at the 1941 settings the energy ledger closes to a hundred-thousandth. Three definitions of its efficiency, one of which would rate an 1804 run at 137 per cent. Finally the simulation is tested against 163 measured runs, and it is shown where it fails.

Most pumps need something to push them: a motor, a windmill, an arm. This one needs only a stream with a small fall. Water runs down a pipe and out of a valve at the bottom until it is moving fast enough to slam that valve shut. Stopped suddenly, the moving column of water squeezes the water ahead of it, and for a fraction of a second the pressure at the bottom is far higher than the fall could ever make by standing still. That pressure pushes a little water through a second valve and up a delivery pipe to a tank on the hill. Then the column rebounds, the first valve drops open, and it all begins again, about once a second, for as long as the stream runs.

It is called a hydraulic ram, and the thing to notice before you touch it is the price. The water that climbs is paid for with the water that is thrown away.

What you are watching: the ram Lansford and Dugan tested at the University of Illinois (a Rife No. 20B with a 54.8 ft drive pipe of 0.0233 sq ft bore, which is 16.7 m and 52.4 mm), at their supply head of 9.2 ft (2.8 m) and one of their valve settings. The drive pipe is coloured by pressure, blue for still water and hot for water squeezed well above the supply head. The trace below it is the pressure inside the ram body and the water speed at the valve. The readouts under the controls are not taken from the animation: they come from running the same engine to a steady rhythm and averaging over whole beats, so they do not depend on your screen.

One beat, slowed down

Set the time to five hundred times slower and watch a single beat. The valve starts to shut when the water reaches the speed you chose with the third slider, and as it shuts the pressure in the body climbs. The moment the pressure passes the height of the delivery tank, the delivery valve opens, and here is the part the sound hides. The pressure does not spike once and fall. It sits at the delivery head while a pressure wave runs up the drive pipe to the supply, is reflected, and runs back, 2L/a = 0.0246 seconds for the round trip in this pipe, and each return knocks the column a little slower. The trace becomes a staircase, and each tread is one more small push of water into the air chamber.

The 1941 engineers saw exactly this on an oscillograph, and it is the second of their conclusions:

“pumping was performed by several rapid pressure waves or impulses of the water in the drive pipe during the pumping period in each cycle (designated as Period 3 in the analysis), and not by one surge as the sound of the operating ram would seem to indicate.”W. M. Lansford and W. G. Dugan, An Analytical and Experimental Study of the Hydraulic Ram, University of Illinois Engineering Experiment Station Bulletin 326 (1941), Conclusions, section 22. They measured the average surge at 0.0245 s against their calculated 0.0251 s.

The man who built the first self-acting ram had said the same thing a hundred and thirty-nine years earlier, in so many words:

“Ainsi on voit que cette pression est bien loin d’être un choc, un coup de marteau”Montgolfier, “Note sur le Bélier hydraulique, et sur la manière d’en calculer les effets”, Journal des Mines vol. 13, p. 45, signed Paris, 8 thermidor an 10 (27 July 1802). In English: “So one sees that this pressure is very far from being a shock, a hammer blow.”

Now push the delivery tank down toward twice the fall and the pump stops with its valve shut. The rebound after each delivery is too weak to drop the pressure in the body enough for the valve to fall open again. A real ram does this, which is why rams are started by pressing the valve down by hand. The same bulletin puts the working range as lifting “to any height from about twice the supply head to many times the supply head”.

The hammer is the engine

The pressure that does the lifting is water hammer, the same bang a pipe makes when a tap is shut too fast. Nikolai Joukowsky measured it on cast-iron water-works pipes in Moscow in 1897, and the rule he found is short enough to hold in one hand: the pressure rise equals the water's density, times the speed of the flow you stopped, times the speed at which a pressure wave runs along the pipe.

“Joukovsky found that P = vλγ/g = vλρ₀, where v = the extinguished velocity of water in the pipe. λ = the speed of propagation of the pressure wave in the pipe”O. Simin, “Water Hammer (with special reference to the researches of Prof. N. Joukovsky)”, Proceedings of the American Water Works Association (1904), p. 365. Joukowsky's memoir is cited there as 1898.

The wave speed is not the speed of sound in open water. The pipe wall stretches as the pressure passes, and a softer wall makes a slower wave, which is why the material matters.

So stopping 0.89 m/s of water in the 1941 steel pipe could raise the pressure by about 123 m of water, far more than the ram needs. Look at the peak readout in the ram above: the body barely rises above the delivery head. The delivery valve opens as soon as the pressure passes it, so the hammer is not spent as one blow but paid out in the staircase of waves, a little at a time.

Now try the polyethylene. The wave slows to a few hundred metres a second and the same stopped flow can raise only a few tens of metres. In the simulation above, choose a plastic drive pipe and raise the tank: once the tank is higher than that hammer head, the first surge cannot open the delivery valve and the flow collapses. That is a result of this model, not a field trial, but it is what the practical manual says in plain words:

“It must be made from good quality steel or iron water pipe - plastic and concrete pipes are useless for drive pipes.”S. B. Watt, A Manual on the Hydraulic Ram for Pumping Water (Intermediate Technology Publications, 1975), section 4.2, p. 8.

The ledger, and three kinds of efficiency

Nothing here is free. The water that falls to the waste valve gives up the height of the fall, and the water that climbs gains the height of the lift above the supply. Energy cannot be made, so the second can never exceed the first: the lifted flow times its extra height is at most the wasted flow times the fall. Every litre that climbs five times higher than it fell costs at least five litres thrown away, and a real ram throws away more. The bar below is the simulation's own account of where the supply's energy went, summed over whole beats, and the last figure is what is left over when every term is subtracted from the input. It is the check that the simulation is not quietly making or losing energy. At the 1941 settings it is about a thousandth of a per cent; push the sliders to extremes, with a soft pipe and a pump that barely pumps, and it can reach one per cent, which is the coarseness of the simulation's grid showing, not a leak in the physics.

Both of those percentages are honest and both are called efficiency. The one on the left is the form in the Indian test code for rams (IS 11390:1985) and in Watt's manual, which rates Blake's rams at “about 65%”. The one on the right is what Lansford and Dugan printed in 1941 and called the Rankine efficiency. They measure different things. The left one counts all the water that went through the pipe, including the water that climbed, and credits the climbers with their whole height above the ram. The right one charges only the water that was thrown away and credits the climbers only with the height they gained above the supply. The left is always the larger of the two, and the gap is widest when the lift is only a few times the fall.

You can see the gap in the 1941 measurements themselves, with no simulation involved. Test 711 of the 2-inch ram, lifting to 24.5 ft from a 9.2 ft fall, has a Rankine efficiency of 28.9% by its own printed flows and 39.4% in the test-code form. Test 703, lifting to 103.5 ft, has 54.8% and 57.1%. Same ram, same valve setting, two numbers.

The argument is older than the test code. Johann Albert Eytelwein ran 1,123 experiments on two rams built for him in Berlin in 1804 and, in 1805, worked three candidate definitions through his own second experiment. The page image is in the sources below; the three results are printed there as 1,3728, 0,9006 and 0,8485.

The first is more than one: the machine appears to deliver 137 per cent of the energy it was given. Eytelwein says that the report Bossut and Cousin made to the Institut on Montgolfier's ram on 30 June 1799 was built on this kind of accounting, and he dismissed it as “absurde” precisely because it exceeds unity. The second is the test-code form. He adopted the third, and gave his reason:

“le rapport d’effet du Bélier, comparé à d’autres machines, obtient la plus petite valeur, et … l’on est d’autant plus assuré de ne présenter dans aucun cas l’effet du Bélier sous un jour trop favorable”J. A. Eytelwein, Observations sur les effets et l’application avantageuse du bélier hydraulique (Paris, 1822; the German original is 1805), §IX, p. 23. In English: the ram's efficiency, compared with other machines, comes out at the smallest value, so one can be surer of never showing the ram in too favourable a light.

His chosen number is the same quantity Lansford and Dugan called the Rankine efficiency, written with the lift measured from the supply rather than from the ram. A number that describes a machine is a choice about what to count, and the choice can be made in the machine's favour or against it. Eytelwein chose against, and said so.

Who invented it

The first machine to raise water by its own momentum was not self-acting. John Whitehurst described it in a letter to Benjamin Franklin, read at the Royal Society on 16 March 1775: a pipe “1½ inch diameter, and nearly two hundred yards in length” from a reservoir to the kitchen offices at Oulton in Cheshire, built in 1772. Every time someone in the kitchen shut the cock, the stopped column opened a valve and forced water into an air vessel. It worked “as often as water is drawn from F”, and the pressure was enough to burst the lead air vessel “in a few months after it was first constructed”. (English Wikipedia says it raised water 4.9 m, which is 16 feet. The letter gives sixteen feet as the fall from the reservoir down to the cock, and gives no lift height at all.)

The self-acting ram, with the waste valve that closes itself and falls open again, is Montgolfier's. His own note says he built it “depuis plus de six ans” before July 1802 at his paper mill at Voiron, using a fall of 10 feet, and that “je déclare que j'en suis le seul inventeur”. He complains there that drawings passed with his consent to Watt and Boulton were copied faithfully into Boulton's London patent of 13 December 1797, and he claims one of his rams compressed air to 40 atmospheres from a 10-foot fall, enough in principle to lift water 1,280 feet. Eytelwein records a French patent of 3 November 1797 to “MM. Montgolfier et Argant”, and names the inventors from the Journal de Paris of 20 January 1798 as “les frères Joseph et Etienne Montgolfier”: Joseph-Michel and Jacques-Étienne, whose hot-air balloon first flew in public at Annonay on 4 June 1783. The 1802 note itself is signed only “Montgolfier”, so the identification rests on Eytelwein's report (English Wikipedia credits Joseph-Michel).

Tested against 163 measured runs

A simulation that only looks right is a drawing. This one was run against every row of the 1941 performance table: 163 tests on two Rife rams, six valve settings, delivery heads from 23.5 to 418 ft, the water wasted and the water pumped in each test weighed on calibrated scales. For each row the engine was given the rig's measured length, bore and wave speed, the row's supply head, delivery head and closing speed, and the valve closure time the bulletin measured for that valve stroke. The friction factor, the entrance loss and the valve coefficients are handbook values set before the table was opened, and none of them was adjusted to it.

One choice was made after looking, and it is declared here. The first run had the waste valve closing at a steady rate, and on the first series it predicted efficiency falling steadily with lift where the measurements stay level. The closure was changed to a disc starting from rest under a steady net force, which closes slowly at first and then fast, and which is how a weighted disc swept up by the flow should move. That change was chosen while looking at Series 1, so Series 1 is not a fair test of it; Series 2 to 6 were not looked at before it was made.

The pattern is the finding. On the 2-inch ram with its closure time measured directly (Series 1 and 2), the simulation's best efficiency lands within two points of the measured best, and it gets the water wasted and pumped per beat within about 10 to 20 per cent. Everywhere the real valve differs from the simulated one it is too optimistic, and in Series 6 its efficiency averages 29 points above the measured one. The 4-inch ram had what the bulletin calls a “soft waste valve disc”, and its authors concluded that “the elasticity of the waste valve cannot be neglected for these rams”; this simulation neglects it. Series 3 to 6 also rest on closure times interpolated or extrapolated from the bulletin's valve records rather than measured for that stroke. The simulation also runs its beats too fast, in 156 of the 162 tests it could settle into a steady beat (one Series 5 test never did, and is left out rather than averaged), as the beat-time column shows, probably because it lets the valve fall open the instant the pressure drops, with no inertia and no bounce.

It misses one thing even on Series 1, and the chart shows it plainly: at the lowest lifts the measured efficiency falls steeply (28.9% at 24.5 ft) while the simulation stays level near 56%. Whatever costs a real ram so much when the lift is only two or three times the fall, this model does not contain it.

So the honest reading is narrow. A one-dimensional water-hammer model with rigid, massless valves reproduces the rhythm and the ceiling of a ram whose valve really is rigid, and it overstates what a ram with a soft or fast valve can do. The losses it is missing live in the valves.

Sources

• W. M. Lansford and W. G. Dugan, An Analytical and Experimental Study of the Hydraulic Ram, University of Illinois Engineering Experiment Station Bulletin 326 (1941). IDEALS, free. Table 2 (pp. 40 to 43), Tables 3 and 4, the worked example on p. 54, conclusions on pp. 65 to 67.
• Montgolfier, “Note sur le Bélier hydraulique, et sur la manière d’en calculer les effets”, Journal des Mines 13 (an 11), pp. 42 to 51. Annales des Mines.
• J. Whitehurst, “Account of a Machine for Raising Water, Executed at Oulton, in Cheshire, in 1772”, Philosophical Transactions 65 (1775), 277 to 279. JSTOR Early Journal Content.
• J. A. Eytelwein, Bemerkungen über die Wirkung und vortheilhafte Anwendung des Stoßhebers (Berlin, 1805); French translation, Observations sur les effets et l’application avantageuse du bélier hydraulique (Paris, 1822), §§IX to XI, pp. 22 to 25. archive.org.
• J. F. D’Aubuisson de Voisins, A Treatise on Hydraulics, trans. J. Bennett (Boston, 1852), §§415 to 419. archive.org.
• O. Simin, “Water Hammer (with special reference to the researches of Prof. N. Joukovsky)”, Proc. American Water Works Association (1904). archive.org.
• S. B. Watt, A Manual on the Hydraulic Ram for Pumping Water (Intermediate Technology Publications, 1975). archive.org.
• Bureau of Indian Standards, IS 11390:1985, Test Code for Hydraulic Rams, §2.4. archive.org.