Note:

This formula calculates the velocity of a liquid using a Pitot tube. It is based on Bernoulli’s principle, which states that an increase in fluid velocity corresponds to a decrease in pressure.

Parameters:

• u₁ (Fluid Velocity): The speed at which the liquid moves through the pipe (m/s).
• ΔP (Pressure Difference): The difference between static pressure and dynamic pressure (Pa).
• ρ (Fluid Density): The mass per unit volume of the liquid (kg/m³).

Constant Parameter

The 2 in the formula comes from Bernoulli’s equation:

When using a Pitot tube, the velocity at the stagnation point (P₂) is zero. Simplifying Bernoulli’s equation results in:

Rearranging for velocity (u₁), we multiply both sides by 2:

This explains why the 2 appears—it accounts for the kinetic energy per unit volume in the system.

Real-Life Applications:

• Fire Safety: Determines water velocity in fire hydrant flow testing.
• Aerodynamics: Used in aircraft to measure airspeed.
• HVAC Systems: Measures air velocity in ventilation and smoke control systems.
• Industrial Piping: Ensures efficient flow in oil, gas, and water pipelines.

Conclusion:

The Pitot tube velocity formula is essential in fluid mechanics. It plays a critical role in industries like fire safety, aviation, HVAC, and oil & gas transport, helping engineers design efficient fluid transport systems.