Question

If \(u\) is velocity of fluid, \(ρ\) is density of fluid, \(L\) is length of the pipe, \(D\) is diameter of the pipe, \(f\) is friction factor and \(△P_1\) is pressure drop, then the equation \(△P_1 = (2fu^2Lρ) ÷ △\) represents

• A. Hagen Poiseuille equation
• B. Bernoulli equation
• C. Fannings equation
• D. Reynolds equation

Answer 1

The Correct Option is C

To determine which equation is represented by \(\Delta P_1 = \frac{2fu^2L\rho}{D}\), let's examine the terms involved:

• \(u\) : Velocity of fluid
• \(\rho\) : Density of fluid
• \(L\) : Length of the pipe
• \(D\) : Diameter of the pipe
• \(f\) : Friction factor
• \(\Delta P_1\) : Pressure drop

The equation in question \(\Delta P_1 = \frac{2fu^2L\rho}{D}\) is designed to calculate the pressure drop in a fluid moving through a pipe due to friction. This form of equation can be identified by comparing it with known correlations for pressure drop in fluid flows:

1. Hagen-Poiseuille Equation: This equation is applicable for laminar flow and is expressed as \(\Delta P = \frac{8\mu Lu}{\pi r^4}\), where \(\mu\) is the dynamic viscosity. It is clearly different from the given equation.
2. Bernoulli's Equation: Bernoulli's Principle deals with the energy conservation in a fluid flow, expressing the relationship between fluid velocity, pressure, and elevation. It does not include a term for friction factor and is therefore not related to the given equation.
3. Fanning's Equation: This equation accounts for the pressure drop due to friction in a pipe. It is expressed as \(\Delta P = 2fu^2L\rho/D\), directly matching the given equation.
4. Reynolds Equation: This is typically related to defining the flow regime using Reynolds number, and not directly concerned with pressure drop due to friction.

Based on the analysis, the given equation directly matches with the Fanning's equation, which is used to calculate the frictional pressure drop in a pipe flow.

Conclusion: The correct answer is Fanning's equation.