# Relationship between hydrostatic pressure and height

The hydrostatic pressure can be determined from a Also, since the height h of the fluid column between z and z0 is often. This video lesson will introduce you to hydrostatic pressure in a liquid, a given area, but the difference is that a fluid's pressure pushes on the walls of the barometric pressure), so we need to know the height of the fluid. We all know that pressure decreases with height, but do you know why? The atmosphere's basic pressure structure is determined by the hydrostatic balance.

Heron's fountain Heron's fountain is a device invented by Heron of Alexandria that consists of a jet of fluid being fed by a reservoir of fluid.

The fountain is constructed in such a way that the height of the jet exceeds the height of the fluid in the reservoir, apparently in violation of principles of hydrostatic pressure. The device consisted of an opening and two containers arranged one above the other. The intermediate pot, which was sealed, was filled with fluid, and several cannula a small tube for transferring fluid between vessels connecting the various vessels.

Trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir. Pascal's contribution in Hydrostatics[ edit ] Main article: Pascal's Law Pascal made contributions to developments in both hydrostatics and hydrodynamics.

### Hydrostatics - Wikipedia

Pascal's Law is a fundamental principle of fluid mechanics that states that any pressure applied to the surface of a fluid is transmitted uniformly throughout the fluid in all directions, in such a way that initial variations in pressure are not changed.

Pressure in fluids at rest[ edit ] Due to the fundamental nature of fluids, a fluid cannot remain at rest under the presence of a shear stress. However, fluids can exert pressure normal to any contacting surface.

If a point in the fluid is thought of as an infinitesimally small cube, then it follows from the principles of equilibrium that the pressure on every side of this unit of fluid must be equal. If this were not the case, the fluid would move in the direction of the resulting force. Thus, the pressure on a fluid at rest is isotropic ; i.

## Hydrostatic Pressure

This characteristic allows fluids to transmit force through the length of pipes or tubes; i. 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.

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.

### Hydrostatic Pressure

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. This does not seem much but when you consider that many pressure sensors can measure to a better precision than 0.

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 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.

Since liquid height derived pressure units have a fixed value, they rarely match the real height measurement of a liquid. This is because the hydrostatic pressure generated by a measured height of liquid will vary depending on the liquid temperature and local gravity.