Darcy Weisbach Calculation

Darcy-Weisbach Equation:

\[ \Delta P = f \left( \frac{L}{D} \right) \left( \frac{v^2}{2g} \right) \rho g \]

Friction Factor (f):

dimensionless

Pipe Length (L):

meters

Pipe Diameter (D):

meters

Flow Velocity (v):

m/s

Fluid Density (ρ):

kg/m³

Pressure Drop (ΔP):

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1. What is the Darcy-Weisbach Equation?

The Darcy-Weisbach equation calculates the pressure drop (head loss) due to friction along a given length of pipe with a constant flow rate. It's widely used in fluid mechanics and hydraulic engineering.

2. How Does the Calculator Work?

The calculator uses the Darcy-Weisbach equation:

\[ \Delta P = f \left( \frac{L}{D} \right) \left( \frac{v^2}{2g} \right) \rho g \]

Where:

\( \Delta P \) — Pressure drop (Pa)
\( f \) — Darcy friction factor (dimensionless)
\( L \) — Length of pipe (m)
\( D \) — Diameter of pipe (m)
\( v \) — Flow velocity (m/s)
\( g \) — Gravitational acceleration (9.81 m/s²)
\( \rho \) — Fluid density (kg/m³)

Explanation: The equation accounts for frictional losses in pipes due to viscosity and pipe roughness.

3. Importance of Pressure Drop Calculation

Details: Calculating pressure drop is essential for designing piping systems, selecting pumps, and ensuring proper fluid flow in industrial and municipal applications.

4. Using the Calculator

Tips: Enter all values in consistent units. The friction factor depends on Reynolds number and pipe roughness - typical values range from 0.01 (smooth pipes) to 0.05 (rough pipes).

5. Frequently Asked Questions (FAQ)

Q1: How to determine the friction factor?
A: For laminar flow (Re < 2000), f = 64/Re. For turbulent flow, use Moody chart or Colebrook-White equation.

Q2: What are typical velocity ranges?
A: Water in pipes: 1-3 m/s (avoid >3 m/s to prevent erosion). Air in ducts: 5-15 m/s.

Q3: Does this work for non-circular pipes?
A: Yes, but use hydraulic diameter (4 × area/perimeter) instead of D.

Q4: What about minor losses?
A: This calculates only major (friction) losses. Add minor losses (valves, bends) separately.

Q5: Valid for compressible flow?
A: Only for incompressible flow. For gases, use modified equations accounting for density changes.