Calculation of Fluid Pressure
Calculation of fluid pressure in static and dynamic fluid is discussed below:
Fluid Pressure in Static Fluids
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 referred 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. In order 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)
Example: Calculate the pressure 10 meters underwater in fresh water (ρ=1000kg/m3 ).
Solution:
Using the formula: P=1000 × 9.81×10 + 101325 = 198100 Pa
This is the total pressure, including the atmospheric pressure.
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 + 1/2ρv2 + ρgh = constant;
where
v = velocity of the fluid (m/s)
This equation shows that in a flowing fluid, the pressure is influenced by both the fluid’s velocity and its height (or depth).
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Fluid Pressure
Liquids and gases play an important role in our life. The earth’s atmosphere is so big as it appears like an ocean of gases. About 76% of the surface of the earth is covered with water. We cannot think of a life without gases (air) and water, Liquids are collectively known as fluids. A substance that flows under the action of an applied force and does not have a shape of its own is known as a liquid. The study of fluids which is at rest is known as hydrostatic or fluid statics. The study of hydrodynamics. In this article, we will have the study of liquids only.