# Hydrostatic Pressure

Hydrostatic pressure is the pressure that is caused by the weight of liquid above a measurement point when the liquid is at rest. The height of a liquid column, of uniform density, is directly proportional to the hydrostatic pressure.

The hydrostatic properties of a liquid are not constant and the main factors influencing it are the density of the liquid and the local gravity. Both of these quantities need to be known in order to determine the hydrostatic pressure of a particular liquid.

The formula for calculating the hydrostatic pressure of a column of liquid in SI units is:

Hydrostatic Pressure (Pa, N/m2) = Height (m) x Density(kg/m3) x Gravity(m/s2)

The density of a liquid will vary with changes in temperature so this is often quoted alongside hydrostatic pressure units e.g. mH2O @ 4 deg C.

The local gravity depends on latitudinal position and height above sea level.

For convenience the most common standard for hydrostatic pressure is metres of water or feet of water at 4 deg C (39.2 degF) with a standard gravity of 9.80665 m/s2. The density of pure water at 4 deg C is very close to 1000 kg/m3 and therefore this has been adopted as the standard density of water. Another reason for the significance of choosing 4 deg C is that it is very close to the temperature that water reaches its maximum density.

In practical terms hydrostatic pressure units are rarely absolutely precise because the temperature of any liquid is not always going to be 4 deg C. You will also come across another temperature standard of 60 deg F (15.56 deg C). This can lead to confusion and inaccuracies when the temperature is not labelled alongside the hydrostatic pressure unit. For most applications these differences are not significant enough to influence the results since the reading accuracy is often much wider than the difference in the pressure unit conversion factor at these 2 temperatures.

In summary hydrostatic pressure units are a very convenient method for relating pressure to a height of fluid but they are not absolute pressure units and it is not always clear what density/temperature has been assumed in their derivation, so be very cautious when using them for high precision level measurements. In fact some institutions are discouraging their use because of the very reasons mentioned above.

## Help

### Pressure generated by gravity fed water system in a house

*How many bars pressure does a gravity fed water system generate? Our house has the water header tank located in the loft. The bathroom is one floor below the cold and hot water tanks.*

The pressure generated by a vented water tank is equal to the difference in water height between the water surface inside the tank (typically near the top when there is no demand) and the measurement point. Since the pressure generated is dependent upon the height of water above the measurement point, the pressure will change at different levels within the house.

- 1 metre of water is approximately equal to 0.098 bar, so the difference in height (m) between the vented/open header water tank and the water tap (faucet) multiplied by 0.098 will equal the pressure in bar.
- 1 foot of water is approximately equal to 0.03 bar, so the difference in height (ft) between the vented/open header water tank and the water tap (faucet) multiplied by 0.03 will equal the pressure in bar.

### Temperature of liquid

*Why is temperature included with height of fluid pressure units?*

Pressure units which are related to the height of a liquid often include a reference temperature e.g. 50 mH2O @ 4degC.

The hydrostatic pressure of a fluid at a certain height is determined by the total height of fluid above that point. If the temperature of the liquid is increased it will expand in volume, thus increasing the fluid level. However the hydrostatic pressure will remain the same, therefore when quoting a pressure in terms of fluid level it is useful to know the temperature.

For example a tank full of water located above ground level on a warm day in the UK might be 28 degC during the middle of the day, whereas during the early hours of the morning it might drop as low as 8 degC. The difference in level due to a 20degC change would be approximately 0.2% without any change in pressure. This does not seem much but when you consider that many pressure sensors can measure to a better precision than 0.25% of full scale a 0.2% change in water density is quite significant.

For applications where you are interested in the weight of the tank contents rather than the volume, a fluid level reading which is independent of changes in density due to temperature variation can actually be very useful.

A hydrostatic pressure unit can be specified for any reference temperature, but to simplify calibration and establish commonality across manufacturers, standardised temperatures are used such as 4 degC (39.2 degF) and 60 degF (15.56 degC).

Many manufacturers do not explain on their product data sheets which temperature they have used, particular with sensors where absolute accuracy is not so important, so if high accuracy is important to your application, calibration should be verified during installation.