Today we continue with Physics, and more specifically the branch of "Classical Mechanics", in order to talk about Measuring Pressure in Fluids.
So, without further ado, let's get straight into it!
Pressure in Fluids
The concept of pressure is defined for both solids and fluids, but is more important when discussing fluids. The main reason being that fluids don't show any significant resistance to the force applied parallel to the surface of the fluid. The exerted force simply compresses or expands the fluid.
Variation with Depth
Considering a fluid of constant density, the pressure at the bottom of it is equal to the atmospheric pressure plus the pressure of the fluid itself due to its weight. The weight is simply equal to it's mass times the acceleration due to gravity.
The weight (force) of the fluid is thus:
In the case of a cylinder fluid container (with a volume V equal to the area A times height h) we have:
So, the pressure at the bottom (basically any depth h) is given by:
Note: Don't confuse pressure p with density ρ
Absolute and Gauge Pressure
When measuring pressure because the atmospheric pressurepatm doesn't change much it makes sense to not include it in the calculations. Measuring equipment thus calculates something known as gauge pressure, pg. The total pressure is referred to as absolute pressure, pabs.
Their relationship is as follows:
Measuring Pressure
Pressure is measured using various devices. Basically any property that changes in a fluid can be used in order to construct a pressure gauge.
A manometer gauges based on the pressure caused by the weight of the fluid. Its quite common for only one side of the U-shaped tube to be open to the atmosphere. Of course, the device supposes that the fluid density is constant and thus simply calculates the value p = hρg.
The change of atmospheric pressure is commonly reported in weather forecasts as barometric pressure. The fluid used in a barometer is often mercury, and so as the atmospheric pressure varies, the mercury rises or falls. Because the atmospheric pressure also varies with altitude such an barometer can also be used as an altitude meter (altimeter).
Example
When an open U-tube is filled with two liquids, the difference in height can tell us about the density of the liquids.
The pressures of the liquids are equal and related follows:
When the density is equal then the individual heights will of course also be equal. Otherwise:
