How Does Fluid Pressure Work? Conditions, Applications & Pascal’s Principle
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.
Pfluid = P + ρgh
Where,
P = Pressure at the reference point
Pfluid = 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:
Pfluid = 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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FAQs on Fluid Pressure: Definition, Formula & Key Principles
1. What is fluid pressure?
Fluid pressure is the force exerted by a fluid, such as a liquid or a gas, per unit area on any surface it is in contact with. This pressure arises from the collective weight and random motion of the fluid's molecules and always acts perpendicular to the surface.
2. What are the main factors that determine the pressure within a fluid?
The pressure at a point within a static fluid is primarily determined by three key factors:
- Depth (h): Pressure increases directly with the depth below the fluid's surface.
- Density of the fluid (ρ): Denser fluids exert more pressure at the same depth because they have more mass in the same volume.
- Acceleration due to gravity (g): The force of gravity acting on the fluid's mass is a crucial component in creating pressure.
3. How is fluid pressure calculated using its formula?
The pressure (P) at a certain depth (h) within a fluid at rest is calculated using the formula: P = P₀ + ρgh. In this equation, P₀ is the pressure at the surface (often atmospheric pressure), ρ (rho) is the density of the fluid, g is the acceleration due to gravity, and h is the depth from the surface.
4. Why is fluid pressure considered a scalar quantity and not a vector?
Fluid pressure is a scalar quantity because it acts equally in all directions at a single point within the fluid. While the force that results from this pressure is a vector (as it has both magnitude and a specific direction, perpendicular to a surface), pressure itself is a magnitude that describes the state of the fluid at that point, without an inherent direction.
5. What is the difference between atmospheric, gauge, and absolute pressure?
These terms describe pressure relative to different reference points:
- Absolute Pressure: This is the total pressure measured relative to a perfect vacuum (zero pressure). It accounts for all pressure sources, including the atmosphere.
- Atmospheric Pressure: This is the pressure exerted by the weight of the Earth's atmosphere at a given location.
- Gauge Pressure: This is the pressure measured relative to the local atmospheric pressure. It is the difference between absolute pressure and atmospheric pressure (P_gauge = P_absolute - P_atm). A car tyre's pressure is a common example of gauge pressure.
6. How does Pascal's Principle relate to fluid pressure?
Pascal's Principle states that a pressure change applied to any part of an enclosed, incompressible fluid is transmitted undiminished to every other part of the fluid and to the walls of its container. This is the core concept behind hydraulic systems like car brakes and lifts, where a small force on a small area generates a large force on a larger area.
7. Why does pressure increase with depth in a fluid?
Pressure increases with depth because the fluid at a lower level must support the weight of the entire column of fluid directly above it. As you go deeper, the height, and therefore the weight, of this fluid column increases. This greater weight exerts a larger downward force on the area below, which is experienced as higher pressure.
8. What are some real-world examples of fluid pressure in action?
Fluid pressure is fundamental to many phenomena:
- Dams: Dams are built much thicker at the base to withstand the immense increase in water pressure with depth.
- Breathing: The process of inhalation and exhalation is driven by pressure differences created between the lungs and the atmosphere.
- Hydraulic Lifts: Car jacks and industrial lifts use Pascal's principle to multiply force through a confined liquid.
- Blood Pressure: The circulation of blood throughout the body is maintained by the pressure created by the heart pumping the blood.
9. How can pressure at the bottom of a container be independent of the container's shape?
This phenomenon, often called the hydrostatic paradox, occurs because pressure at a certain depth depends only on the height of the fluid and its density, not the container's shape or total fluid volume. The force on the bottom of the container is determined solely by the weight of the vertical column of fluid directly above it. In a container with sloped sides, the container walls provide reaction forces that cancel out the horizontal components of pressure, leaving only the vertical component, which depends on depth.
