Fluid pressure is the force exerted by a fluid (liquid or gas) per unit area on the surface of a container or any object placed in the fluid.
- In a fluid at rest, this force always acts perpendicular to the surface.
- Pressure increases with depth and depends on the density of the fluid and the acceleration due to gravity.
Formula
Pressure (P) is defined as the force acting perpendicular to a surface per unit area. If a force F acts normally on a surface of area A, then the pressure acting on the surface is given by:
P = \frac{ Force (F)} {Area (A)}
- P = Pressure
- F = Force acting on the surface
- A = Area of the surface
Factors Affecting
- Depth: Fluid pressure increases with depth, as the weight of the fluid above exerts more force.
- Density of the Fluid: H fluids exert greater pressure at the same depth.
- Gravitational Acceleration: Pressure is directly proportional to gravity, so variations in gravitational force affect fluid pressure.
- Fluid Type: Gases and liquids have different behaviors and responses to pressure changes due to their differing densities.
Units of Pressure
- In the CGS system, the unit of pressure is dyne cm-2.
- In SI, the unit of pressure is Nm-2 or Pascal (Pa)
- Dimensional Formula of Pressure is [ML-1T-2]
Device for Measuring
A simple device used to measure pressure in a fluid is shown below. It consists of an evacuated cylinder. A piston of area 'A' is fitted into the cylinder. A spring is connected between the piston and the bottom of the cylinder.
When the device is submerged in a fluid, the fluid exerts a force (F) on the piston. As a result of this downward force, the spring is compressed as long as the downward force exerted by the fluid on the piston is equal to the upward force exerted by the spring on the piston. The force exerted by the fluid can be determined by calibrating the compression of the spring with a known force. Therefore, the pressure in a fluid can be determined using the relation,
P
= \frac{F}{A}.
Pressure is a scalar quantity. A definite direction is not associated with pressure because hydrostatic pressure is transmitted equally in all directions when force is applied.
Calculation
Static Fluid Pressure
For a static fluid, the stress at any level is a feature of the intensity of the fluid and the density of the fluid. Gravitational discipline i to as (ρ), and gravitational acceleration (g). As the depth grows, the fluid stress rises as the strain of the overlying fluid squeezes the fluid. To decide the strain at the given intensity,
P = ρgh + Patm
Where,
- ρ (rho) = density of the fluid (kg/m³)
- g = acceleration due to gravity (≈9.81 m/s2 on Earth)
- h = depth below the surface of the fluid (m)
- Patm = atmospheric pressure at the surface (≈ 101,325 Pa at sea level)
Dynamic Fluid Pressure
For fluids in motion, calculating pressure can be more complex and typically involves principles from dynamics like Bernoulli’s Equation, which relates pressure, velocity, and elevation:
P + \frac{1}{2}ρv^2 + ρgh = constant
Where,
- v is Velocity of Fluid (m/s)
- ρ (rho) = density of the fluid (kg/m³)
- g = acceleration due to gravity (≈9.81 m/s2 on Earth)
- h = depth below the surface of the fluid (m)
- Patm = atmospheric pressure at the surface (≈ 101,325 Pa at sea level)
This equation shows that in a flowing fluid, the pressure is influenced by both the fluid's velocity and its height (or depth).
Pascal's Law
Pascal's Principle (or Pascal's Law) applies to static fluids, using the relationship between pressure and height in such fluids. It allows the use of fluid pressure, as a measure of energy per unit volume, to perform work, such as in hydraulic presses.
Pascal’s Principle states that in a confined static liquid, any pressure change is transmitted equally throughout the fluid. Pascal’s Law can be derived from the equation that calculates pressure at a specific height or depth within the fluid.
The equation for pressure at a specific height or depth in a fluid is given by:
P = P0 + ρgh
Where;
- P is the pressure at a depth h,
- P0 is the atmospheric pressure (or pressure at the surface),
- ρ is the density of the fluid,
- g is the acceleration due to gravity,
- h is the depth below the surface of the fluid.
This equation reflects how pressure increases with depth in a fluid due to the weight of the fluid above. Pascal's Law is based on this principle, stating that any pressure change applied to an enclosed fluid is transmitted uniformly throughout the fluid.