Flow Loss Coefficient - Rectangular Pipe

- \( a_0\) - channel width
- \( b_0\) - channel height
Rectangular channels are commonly used in open-channel flow systems, HVAC ducts, irrigation canals, and drainage applications. This page provides pressure loss coefficient (K-factor) data specific to rectangular cross-sections and helps calculate flow losses based on channel geometry.
While round cross-sections are more widely documented, rectangular channels require special consideration due to non-uniform velocity profiles and corner effects. Use this tool to determine the flow loss coefficient and compute the equivalent hydraulic diameter for energy loss estimations.
For pipes of rectangular cross section, the flow loss coefficient is defined as:
$$ \lambda = \frac{\Delta p}{(\rho w_0^2 /2)(\ell/D_0)} = k_\mathrm{rec}\lambda_\mathrm{round}$$
where \( \lambda_\mathrm{round}\) is the flow loss coefficient of an equivalent channel of round cross section. See associated calculators for a round channel that is smooth, has uniform sand grain roughness, or has non-uniform roughness.
An equivalent hydraulic diameter for a rectangular channel:
$$ \mathrm{D}_H = \frac{4A}{P} = \frac{2a_0 b_0}{a_0 + b_0} $$
where \( A \) is cross sectional area, and \( P \) is the perimeter
Reynolds number is based on the hydraulic diameter:
$$ \mathrm{Re} = \frac{V \mathrm{D}_H}{\nu}$$
For laminar flow regime (\( \mathrm{Re} \lt 2000 \)):
\( b_0/a_0 \) | 0 | 0.1 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
---|---|---|---|---|---|---|---|
\( k_\mathrm{rect} \) | 1.50 | 1.34 | 1.20 | 1.02 | 0.94 | 0.90 | 0.89 |
For turbulent flow regime (\( \mathrm{Re} \gt 2000 \)):
\( b_0/a_0 \) | 0 | 0.1 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
---|---|---|---|---|---|---|---|
\( k_\mathrm{rect} \) | 1.10 | 1.08 | 1.06 | 1.04 | 1.02 | 1.01 | 1.00 |