# How is the pressure of an incompressible fluid measured?

I've googled around and can't find quite what I'm looking for.. this may be a VERY basic question, but I'd appreciate if it could be explained in layman's terms..

Traditional fuel injection engines have the ability to pressurize a fuel line to ~50psi.

Gasoline Direct Injection/Diesel engine fuel pumps can pressurize a fuel line to 30,000psi or more.

Power washers can pressurize water to 4,000psi +

but all these fluids are 'assumed to be incompressible'...

The explanation that the measured pressure is the force on external walls of a reservoir under pressure doesn't quite make sense to me, in that in order for a High-Pressure fuel reservoir to be under greater than atmospheric (30,000 psi) pressure, the fluid within must also be pressurized.

I don't understand!

I've read that the 'assumption' of incompressibility is not entirely true, but for a liquid to be compressible to 2000bar, the 'assumption' must be entirely false!?

The explanation that the measured pressure is the force on external walls of a reservoir under pressure doesn't quite make sense to me, in that in order for a High-Pressure fuel reservoir to be under greater than atmospheric (30,000 psi) pressure, the fluid within must also be pressurized.

The measured pressure is not a force but it is related to force.

Pressure is the force a fluid exerts on the walls of a container (for instance) expressed per unit of surface area:

$\Large{p=\frac{F}{A}}$, with $p$ the pressure, $F$ the force and $A$ the surface area.

In S.I. units, for example $10 \text{ Pa}$ ($10 \text{ Pascal}$) means the pressure exerts $10 \text{ N}$ ($10 \text{ Newton}$) of force $F$ per $m^2$ of surface area $A$.

[...] in that in order for a High-Pressure fuel reservoir to be under greater than atmospheric (30,000 psi) pressure, the fluid within must also be pressurized.

That is correct.

I've read that the 'assumption' of incompressibility is not entirely true, but for a liquid to be compressible to 2000bar, the 'assumption' must be entirely false!?

I think you may not understand incompressibility completely. Liquids are quasi-incompressible because when you apply pressure on them their volume almost doesn't change. Mathematically we can write:

$\frac{\Delta V}{\Delta p} \approx 0$, where $\Delta V$ is the decrease in volume for a given increase in pressure $\Delta p$. So even for high pressures like $2000 \text{ bar}$ the decrease in volume is quite small (but not quite zero either).

As regards your title question, pressure is measured by means of a manometer.

• Thanks. I guess I assumed the (significant) increase in mass for a given volume when compressing gases would also occur when compressing liquids.. but that obviously doesn't make sense. the quasi-incompressible explanation does - in other words the mass of pressurized liquid in a given volume does increase, just not very much. – goofology Oct 11 '15 at 16:54
• @goofology: one clarification: mass is not affected by pressure at all. What you mean is density: $\rho=\frac{m}{V}$. In gases for instance an increase in $p$ brings about a significant decrease in volume $V$, so $\rho$ then increases. In most liquids this effect is negligible. – Gert Oct 11 '15 at 17:12