Pressure in Fluids at Rest:

Pressure in a fluid at rest is the force exerted by the fluid per unit area on an imaginary surface within the fluid. It acts equally in all directions, and its magnitude increases with depth in a fluid.
Mathematical Form:

P=ρ⋅g⋅h

Where:

  • P is the pressure,
  • ρ is the density of the fluid,
  • g is the acceleration due to gravity,
  • h is the depth of the fluid.
  • Pressure increases with depth due to the weight of the overlying fluid.
  • The pressure at a specific depth is the same in all directions.
  • Pressure is a scalar quantity (magnitude only), and its unit is pascal (Pa) or N/m².

Pressure in Fluids in Motion (Bernoulli's Principle):

In a moving fluid, pressure is influenced by the fluid's velocity. Bernoulli's Principle states that as the speed of a fluid increases, its pressure decreases, and vice versa. This principle is based on the conservation of energy in fluid flow.
Mathematical Form (Bernoulli's Equation):

P+1/2​ρv2+ρgh=constant

Where:

  • P is the pressure,
  • ρ is the density of the fluid,
  • v is the fluid velocity,
  • g is the acceleration due to gravity,
  • h is the height above a reference point.
  • The sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline.
  • As fluid speed increases (velocity increases), pressure decreases, and vice versa.
  • Bernoulli's Principle is often applied to explain lift in aerodynamics, blood flow in arteries, and various engineering applications.

Real-Life Examples:

  1. Dam Construction:
    • At Rest: Pressure increases with depth due to the weight of the water.
    • In Motion: Bernoulli's Principle is considered in designing spillways and optimizing flow.
  2. Airplane Wings:
    • At Rest: Air pressure decreases with altitude.
    • In Motion: Bernoulli's Principle explains lift, where faster air above the wing results in lower pressure compared to slower air below.
  3. Blood Circulation:
    • At Rest: Blood pressure increases with depth in the circulatory system.
    • In Motion: Bernoulli's Principle is relevant in understanding blood flow velocity and pressure variations.

Further Reading