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Bernoulli's Equation Multiplied Throughout by 'pg' Calculator

Pressure at Point 1 (P1) in Pascals:

Pressure at Point 2 (P2) in Pascals:

Height at Point 1 (h1) in meters:

Height at Point 2 (h2) in meters:

Velocity at Point 1 (u1) in m/s:

Velocity at Point 2 (u2) in m/s:

Fluid Density (ρ) in kg/m³:

Note:

Bernoulli’s Equation: It states that in a steady, incompressible, and non-viscous fluid flow, the total mechanical energy (sum of pressure energy, kinetic energy, and potential energy) remains constant along a streamline.

Key Terms:

P1 and P2: Pressure at two different points in the system.
h1 and h2: Height of the fluid at two points (measured from a reference level).
u1 and u2: Velocity of the fluid at two points.
ρ (Density): The mass per unit volume of the fluid (kg/m³).
g (Gravity): Standard gravitational acceleration (9.81 m/s²).

Assumptions in Bernoulli’s Equation:

The fluid is incompressible.
The flow is steady (no changes over time).
No energy is lost due to viscosity (frictionless flow).
The equation applies along a streamline.

Real-Life Applications:

Aerodynamics: Bernoulli’s principle explains how airplane wings generate lift. Faster airflow over the wing reduces pressure, allowing the plane to rise.
Carburetors in Automobiles: Controls the air-fuel mixture using pressure differences.
Venturi Effect: Used in medical devices like oxygen masks and atomizers.
Water Flow Measurement: Used in devices like Venturi meters and Pitot tubes to measure fluid speed.
Fire Sprinkler Systems: Utilizes pressure variations to distribute water effectively.
City Water Supply Systems: Helps in designing pipelines for efficient water distribution.

Limitations of Bernoulli’s Principle:

Does not account for energy losses due to friction or turbulence.
Only valid for streamline (non-turbulent) flow.
Does not apply to highly viscous fluids like honey or oil.

Conclusion:

Bernoulli’s principle is fundamental in fluid mechanics and plays a significant role in engineering applications. It helps predict pressure, velocity, and height relationships in a fluid system, leading to innovations in transportation, medical devices, and industrial fluid control.