Understanding Hydrostatic Pressure

Hydrostatic level transmitter
(Drexelbrook)

Pressure measurement is an inferential way to determine the height of a column of liquid in a vessel in process control. The vertical height of the fluid is directly proportional to the pressure at the bottom of the column, meaning the amount of pressure at the bottom of the column, due to gravity, relies on a constant to indicate a measurement. Regardless of whether the vessel is shaped like a funnel, a tube, a rectangle, or a concave polygon, the relationship between the height of the column and the accumulated fluid pressure is constant. Weight density depends on the liquid being measured, but the same method is used to determine the pressure.

A common method for measuring hydrostatic pressure is a simple gauge. The gauge is installed at the bottom of a vessel containing a column of liquid and returns a measurement in force per unit area units, such as PSI. Gauges can also be calibrated to return measurement in units representing the height of liquid since the linear relationship between the liquid height and the pressure. The particular density of a liquid allows for a calculation of specific gravity, which expresses how dense the liquid is when compared to water. Calculating the level or depth of a column of milk in a food and beverage industry storage vessel requires the hydrostatic pressure and the density of the milk. With these values, along with some constants, the depth of the liquid can be calculated.

The liquid depth measurement can be combined with known dimensions of the holding vessel to calculate the volume of liquid in the container. One measurement is made and combined with a host of constants to determine liquid volume. The density of the liquid must be constant in order for this method to be effective. Density variation would render the hydrostatic pressure measurement unreliable, so the method is best applied to operations where the liquid density is known and constant.

Interestingly, changes in liquid density will have no effect on measurement of liquid mass as opposed to volume as long as the area of the vessel being used to store the liquid remains constant. If a liquid inside a vessel that’s partially full were to experience a temperature increase, resulting in an expansion of volume with correspondingly lower density, the transmitter will be able to still calculate the exact mass of the liquid since the increase in the physical amount of liquid is proportional to a decrease in the liquid’s density. The intersecting relationships between the process variables in hydrostatic pressure measurement demonstrate both the flexibility of process instrumentation and how consistently reliable measurements depend on a number of process related factors.

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