Fluid Pressure

The pressure is a scalar quantity that is defined as force per unit area where the force acts in a direction perpendicular to the surface. Pressure is an important physical quantity—it plays an essential role in topics ranging from thermodynamics to solid and fluid mechanics. Depending on the context of use there are several in which pressure can be expressed.

Fluid pressure can be defined as the measurement of the force per unit area on a given object on the surface of a closed container or in the fluid. Gravity, acceleration, or forces outside a closed container are the factors that cause this pressure.

Fluid Pressure Formula

The following relation can be used to calculate the pressure in fluids.

P_fluid = P + ρgh

Where,

P   = Pressure at the reference point

P_fluid  = Pressure at a point taken in fluid

Ρ   =  Density of the fluid

g   = Acceleration due to gravity (considering earth g = 9.8 m/s)

h   = Height from the reference point

On dividing the mass of the fluid in consideration with the volume of fluid considered, the density of the fluid can be calculated:

ρ = m/v

Where,

m =  mass of the fluid

v = volume of fluid considered

The total pressure on the system is given as follow if the fluid is subjected to atmospheric pressure:

P_fluid = Po + ρgh

Where,

Po = the atmospheric pressure

Conditions for the Consideration of Fluid Pressure:

• In an open condition or open channel flow

• In a closed condition or closed conduit

The Pressure at any Point in a Static Fluid 

Within a static fluid at a given point in space, the sum of acting forces must be equal to zero. The condition for static equilibrium would otherwise not be met. Consider a rectangular region within the fluid medium with density ρL (same as that of the fluid medium), width w, length l, and height h for analyzing such a simple system. Then, within the medium, the forces acting in this region are taken into account. Firstly, a force of gravity acting downwards (its weight) in the region is equal to its density object (ρ), times its volume of the object (v), times the acceleration due to gravity (g). Due to the fluid above the region, the downward force acting on this region is equal to the pressure times the area of contact. Likewise, due to the fluid below the region, there is an upward force acting on this region which is equal to the pressure times the area of contact. The sum of these forces must be zero to achieve static equilibrium. The pressure from the fluid below the region must be greater than the pressure from the fluid above by the weight of the region, for any region within a fluid, to achieve static equilibrium.

Pascal’s Principle

Pascal’s Principle (also known as Pascal’s Law ) is applied to the static fluids and in static fluids takes advantage of the height dependency of pressure. Pascal’s Principle can be used in exploiting the pressure of a static liquid as a measure of energy per unit volume to perform a given work such as in hydraulic presses. 

Pascal’s Principle qualitatively states that in an enclosed static liquid pressure is transmitted undiminished. Pascal’s Law quantitatively within a fluid can be derived from the expression that determines the pressure at a given height (or depth) and is defined by Pascal’s Principle:

p₂=p₁+ Δp 

Δp=ρgΔh

Where,

p₁ =  externally applied pressure 

ρ  =  density of the fluid

Δh = difference in height of the static liquid

g  = acceleration due to gravity

Did You Know?

Pressure is also responsible for the breathing mechanism and plays an essential role in the respiratory system. Inhalation is a result of pressure differences between the lungs and the atmosphere that create a potential for air to enter the lungs. The mechanism resulting in inhalation is due to the lowering of the diaphragm, which increases the volume of the thoracic cavity surrounding the lungs, thus lowering its pressure as determined by the ideal gas law. The reduction in pressure of the thoracic cavity, which normally has a negative gauge pressure, thus keeping the lungs inflated, pulls air into the lungs, inflating the alveoli and resulting in oxygen transport needed for respiration. As the diaphragm restores and moves upwards, the pressure within the thoracic cavity increases, resulting in exhalation. The cycle repeats itself, resulting in respiration which as discussed is mechanically due to pressure changes. Essential functions such as blood circulation and respiration would not have been possible without pressure in the body, and the corresponding potential that it has for dynamic bodily processes.

At a Glance

Fluid pressure can be defined as the pressure observed at a place in the fluid that arises due to the fluid’s weight. It occurs in two scenarios. First, when there is an open channel flow or an open condition. Second, it occurred in a closed condition or flow. The fluid pressure is also called static fluid pressure or hydrostatic pressure which takes into consideration the fluid’s depth. The pressure is negligible when considering the movement of the fluid. This means that the static fluid pressure is independent of surface area, the shape of the container in which the fluid is present, and the mass or volume of the liquid. One must note that ‘fluid’ is defined as the ability to flow by a substance and this can be about both gases and liquids.

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