Flow in Pipes: Fundamentals & Losses

Pipe flow describes liquid flow in a closed conduit where the liquid fills the cross-section.

Flow Regimes

The flow regime is determined by the Reynolds Number ($Re$):

$Re = \frac{\rho V D}{\mu} = \frac{V D}{\nu}$

• Laminar Flow: $Re < 2000$. Viscous forces dominate. Fluid moves in parallel layers.
• Transitional Flow: $2000 < Re < 4000$.
• Turbulent Flow: $Re > 4000$. Inertial forces dominate. Chaotic mixing.

Friction Losses (Major Losses)

Energy loss due to friction along the pipe length ($h_f$).

Darcy-Weisbach Equation

The most accurate method for calculating head loss.

$h_f = f \frac{L}{D} \frac{V^2}{2g}$

• $f$ = Darcy friction factor (dimensionless)
• $L$ = Pipe length
• $D$ = Pipe diameter

Finding $f$:

• Laminar: $f = 64/Re$
• Turbulent: Use the Moody Chart or Colebrook-White equation. Depends on $Re$ and Relative Roughness ($\epsilon/D$).

Minor Losses

Losses due to components like valves, bends, and entrances.

$h_m = K \frac{V^2}{2g}$

• $K$ = Loss coefficient (empirical).

Solved Problems