Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Compliance — where it appears

The give of a system under pressure: how much its volume changes for a given change in pressure. In a pipeline it is the elasticity of the water and the wall, or a pocket of gas, and it sets how fast a pressure wave travels and how a pulse is cushioned.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Gas takes the top off a tall, brief pulse. The head at a closed valve against time, for a line whose margin to vapour pressure is 0.49 Joukowsky rises: the exact vapour-cavity history, whose first pulse after the collapse reaches 1.94 rises for only 0.028 of a round trip, and the same line with a pocket of free gas at the valve of a millionth, a hundred-thousandth and a ten-thousandth of the pipe's volume. A hundred-thousandth brings the pulse down to 1.62: the pocket cannot be squeezed fast enough to follow a pulse that short.

Air at a valve softens the hammer only in quantity

A vapour cavity at a closed valve holds the head at one value, and that is why the pressure after it collapses climbs a staircase of equal steps. Put a pocket of free air there instead and the valve becomes a spring. A millionth of the pipe's volume trims only the tallest, briefest pulses; a hundred-thousandth takes a third off them and moves them; a ten-thousandth can make the pulse taller than it was, even on a line that never cavitates. The air that reliably removes the hammer is a thousandth of the pipe, which is a deliberate air vessel rather than a little dissolved gas.

applied · Water hammer Air that comes out fast makes the first pulse taller. The head at the closed valve of a 600 m main, in Joukowsky rises above its steady head, for eight round trips after the valve shuts, with the water saturated with air at atmospheric pressure. With no release the cavity is vapour and the first pulse is 1.3 rises. If all the water gives up its air slowly, over ten round trips, the gas cushions the collapse and the pulse is 1.16. If it comes out fast, in three-hundredths of one, the cavity holds the head near atmospheric pressure rather than the vapour pressure, it lasts a round trip longer, and the pulse is 1.46 — the air-cavity limit's 1.45.

The air a cavity releases is capped by the cavity

When a shut valve pulls the pressure behind it down, the air dissolved in the water starts to come out, and a little gas was already known to soften the hammer. But air leaves the water only while its pressure in the cavity is below the pressure the water was saturated at, so a cavity can fill with at most its own volume of air at that pressure — a seven-thousandth of the pipe here, however much water gives up its air and however fast. That is less than a third of what removes the hammer. Released quickly, the air does not cushion the collapse at all: it turns the vapour cavity into an air cavity, and the pulse becomes the column-separation pulse with the margin measured to the atmosphere — taller, on this main.

applied · Water hammer

Named alongside it

The objects these essays reach for when they reach for this one.

CavitationColumn-separationMethod of characteristicsModel limitReflectionVapour pressureWater hammerCharacteristicsDimensionlessMeasurementSurge tankWave speed

All concepts