Hydrostatic Pressure

The word hydro relates to fluid, while the word static refers to something that is motionless. As a result, hydrostatics is a branch of fluid mechanics that studies the characteristics of a fluid at rest as well as the pressure produced by the fluid on an object immersed in it, among other things. This is the reason why hydrostatics is also referred to as fluid statics in some circles. In the presence of fluids in an equilibrium state, it is possible to investigate and monitor the properties of those fluids more effectively. It is the pressure produced by the molecules of the fluid as a result of the gravitational force that exists within them or between the molecules and the walls of the container, and it is measured in Pascals.

Hydrostatic pressure 

Hydrostatic pressure can be defined as the pressure exerted by a fluid in equilibrium at a given place within the fluid due to the force of gravity at a given point within the fluid. Hydrostatic pressure can be calculated as As the weight of the fluid increases with the application of a downward force, the hydrostatic pressure is proportional to the depth measured from the surface of the fluid.

Fluid pressure can be created by gravity, acceleration, or other forces when a container is closed off to prevent leakage. 

Derivation of the Formula of Hydrostatic Pressure

Consider a column of water with a total volume of V and an area of A at the base.

W = mg is the weight of water.

We know that the mass of water is equal to the density of water multiplied by the volume X. As a result, w=ρVg

Volume is calculated by multiplying the height by the surface area. 

As a result, V = Ah 

W = ρAhg

By applying the pressure formula: 

p=F/A

p=ρhg

h- the height of fluid above the object

ρ-is the density of the fluid 

g- acceleration due to gravity 

Instruments used to measure hydrostatic pressure 

Hydrostatic gauge

Hydrostatic gauges, like the mercury column manometer, measure pressure and compare it to the hydrostatic force per unit area at the bottom of a column of fluid. Hydrostatic gauges don’t care what kind of gas they’re measuring, and they can be made to be very accurate.

Manometer 

Instruments that compare pressures are called differential manometers, and the simplest one is a U-tube filled with liquid. There are two pressures of interest, p1 and p2. The two pressures are sent to the two ends of the liquid column through an inert gas, and the difference in height, h, of the two menisci is measured. It is given by.

p1-p2=ρgh

Real-life examples of hydrostatic pressure 

• Measure volume

Calculating the volume of an object with perfect geometry is easy because there are formulas that have been proven to work. These formulas give the volume with high precision and accuracy as an output. However, it’s hard to figure out how much space an object takes up if it has a great number of different shapes and sizes. One of the best ways to figure out how big an object is to use hydrostatic force. It is done by putting the object in a container of water and measuring how much water it moves. If you put your body in the container, it moves the water around so that its volume changes.

• Geophysics 

A lot of mud engineering is done with hydrostatic force. For example, in a container that’s full of fluid and one point has a certain amount of pressure, the force there comes from the pressure above that point. It’s important to make sure the hydrostatic force is just right before starting a very common geophysics operation called the mud drilling process. The fluid static force must be strong enough to keep fluids from coming in from the bottom. So the hydrostatic force must not be too high, which can break pipes and cause them to become clogged up with debris.

• Submarines 

Submarines are watercraft that can be used both above and below the surface of the water. The hydrostatic theory and Archimedes’ Principle are the main factors that determine how a submarine works. There are three ways that a submarine can be buoyant, depending on the strength of the buoyancy force and how much weight it has. Underwater, when a submarine is at rest, its weight should be equal to its buoyancy force. As the submarine sinks in the water, the hydrostatic pressure it feels grows. Pumps and sensors are used to make sure that the pressure inside the submarine is equal to the pressure outside. The maximum depth at which a submarine can be used is determined by how well the pumps and other pressure equipment can keep internal pressure high enough to counteract the pressure from the water outside. Thus, knowing the hydrostatic pressure on a submarine is very important when it comes to designing and operating it.

Conclusion 

Hydrostatic pressure can be defined as the pressure exerted by a fluid in equilibrium at a given place within the fluid due to the force of gravity. It is the pressure produced by the molecules of the fluid as a result of the gravitational force that exists within them or between the molecules and the walls of the container. Hydrostatic gauges measure pressure and compare it to the hydrostatic force per unit area at the bottom of a column of fluid. Calculating the volume of an object with perfect geometry is easy because there are formulas that have been proven to work. However, it’s hard to figure out how much space an object takes up if it has a lot of different shapes and sizes.

Hydrostatic theory and Archimedes’ Principle are the main factors that determine how a submarine works. The maximum depth at which a submarine can be used is determined by how well the pumps and other pressure equipment can keep internal pressure high enough to counteract the pressure from the water outside.