Cavitation Number (Margin above Vapour Pressure)

Put the cavitation number and the Euler number side by side. One is $\Delta p/\rho v^2$. The other is $(p - p_v)/\tfrac{1}{2}\rho v^2$. Strip the units off both and they are the same group: a pressure difference divided by a dynamic pressure. Dimensional analysis cannot tell them apart, and that is worth sitting with for a moment.

Buckingham's theorem hands you a pressure group. It does not tell you to put $p - p_v$ on top rather than $p_1 - p_2$, because it knows nothing about vapour pressure, or boiling, or the fact that a liquid has a floor below which it stops being a liquid. That knowledge comes from physics, and the choice of numerator encodes a question: Euler asks how much pressure this component costs me. Cavitation asks how close this flow is to boiling. Same algebra, different engineering. Dimensional analysis organises understanding; it does not supply it.

The mechanism is straightforward and the damage is not. Where a flow accelerates — around a blade leading edge, through a valve seat, at a pump impeller eye, over a hydrofoil — the static pressure falls. If it falls to the vapour pressure of the liquid, vapour cavities form. They are carried downstream into a region of higher pressure and collapse, and the collapse is violent: a bubble imploding near a solid surface does so asymmetrically, driving a microjet at the wall at speeds measured in hundreds of metres per second. Repeat that a few million times and steel pits, bronze erodes, and a pump impeller that looks sandblasted comes out of service.

There is no universal critical value, and anyone who quotes one is quoting a geometry. Incipient cavitation occurs when the cavitation number equals the magnitude of the geometry's minimum pressure coefficient — roughly 0.2 for a well-designed hydrofoil, 1 to 2 for a blunt body, several for a sharp-edged throttling valve. The threshold is a property of the shape. Worse, it is not even a single number for a given shape: nuclei content, dissolved gas, surface finish and the residence time at low pressure all move it, which is why the number at which cavitation appears as you speed up differs from the number at which it disappears as you slow down. Incipient and desinent cavitation numbers bracket a hysteresis loop.

Two input traps. $p$ is an absolute pressure. A gauge reading entered here makes the margin look about 101 kPa smaller than it is, which is a conservative error and still an error. And $p_v$ moves fast with temperature: water goes from 2.34 kPa at 20 °C to 7.38 kPa at 40 °C to 101.3 kPa at 100 °C. A system that never cavitates in winter can cavitate reliably in August, and a hot-water pump has a fraction of the margin the same pump has on cold service.

The pump trade expresses the identical margin as NPSH available, a height in metres rather than a ratio, and the two are the same statement. The dimensionless form travels better between geometries; the head form is easier to compare against a manufacturer's curve. Use whichever the person you are talking to uses, and know that they are the same calculation.