Major Loss Ducts Tubes

Reference data and engineering information about major loss ducts tubes for fluid mechanics applications.

majorlossductstubes

Overview

Engineering reference data for Major Loss Ducts Tubes in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Absolute Roughness - k - for Common Pipe and Duct Materials
Surface	Absolute Roughness - k(10⁻³ m)	Absolute Roughness - k(feet)
Copper, Lead, Brass, Aluminum (new)	0.001 - 0.002	3.3 - 6.7×10⁻⁶
PVC & Plastic Pipes	0.0015 - 0.007	0.5 - 2.33×10⁻⁵
Epoxy, Vinyl Ester & Isophthalic pipe	0.005	1.7×10⁻⁵
Stainless steel, bead blasted	0.001 - 0.006	(0.00328 - 0.0197) 10⁻³
Stainless steel, turned	0.0004 - 0.006	(0.00131 - 0.0197) 10⁻³
Stainless steel, electropolished	0.0001 - 0.0008	(0.000328 - 0.00262) 10⁻³
Steel commercial pipe	0.045 - 0.09	1.5 - 3×10⁻⁴
Stretched steel	0.015	5×10⁻⁵

Energy Balance & Pressure Loss

The energy equation for steady, incompressible flow between two points states that the upstream energy equals the downstream energy plus the loss between them. This is expressed in two common forms:

Pressure Form (Energy Balance): $p_1 + \frac{\rho v_1^2}{2} + \rho g h_1 = p_2 + \frac{\rho v_2^2}{2} + \rho g h_2 + \Delta p_{\text{loss}}$

Head Form (Energy Balance): $\frac{p_1}{\gamma} + \frac{v_1^2}{2g} + h_1 = \frac{p_2}{\gamma} + \frac{v_2^2}{2g} + h_2 + \Delta h_{\text{loss}}$

For a horizontal, steady-state flow ( $v_1 = v_2$ , $h_1 = h_2$ ), these simplify to: $\Delta p_{\text{loss}} = p_1 - p_2 \quad \text{and} \quad \Delta h_{\text{loss}} = \frac{p_1 - p_2}{\gamma}$

Head Loss Components

Total head loss ( $\Delta h_{\text{loss}}$ ) comprises two parts:

Major (Friction) Head Loss: $\Delta h_{\text{major\_loss}} = \lambda \frac{l}{d_h} \frac{v^2}{2g}$

Minor (Dynamic) Head Loss: $\Delta h_{\text{minor\_loss}} = \xi \frac{v^2}{2g}$

Flow Regimes & Friction Coefficient (λ)

The friction coefficient ( $\lambda$ ) depends on the flow regime, determined by the Reynolds number ( $Re$ ).

Laminar Flow ( $Re < 2300$ ): $\lambda = \frac{64}{Re}$ Roughness is negligible; $\lambda$ depends only on $Re$ .
Transitional Flow ( $2300 < Re < 4000$ ): The flow oscillates between laminar and turbulent; $\lambda$ is not reliably predictable.
Turbulent Flow ( $Re > 4000$ ): $\lambda$ depends on both $Re$ and the relative roughness ( $k/d_h$ ). It is determined empirically: $\lambda = f\left(Re, \frac{k}{d_h}\right)$

The minor pressure loss for components like bends, valves, and fittings is calculated as: $\Delta p_{\text{minor\_loss}} = \xi \frac{\rho v^2}{2}$ Where $\xi$ is the minor loss coefficient, unique to each component type and geometry.

References

Original Source

Source: engineeringtoolbox.com