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Minor Pressure Loss Ducts Pipes

Reference data and engineering information about minor pressure loss ducts pipes for fluid mechanics applications.

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Overview

Minor pressure losses occur at pipe fittings, valves, bends, tees, expansions, and contractions. Although called 'minor', these losses can be significant in short piping systems.

Variables

SymbolDescriptionUnit
KKMinor loss coefficient—
ΔP\Delta PPressure dropPa
LeqL_{eq}Equivalent pipe lengthm

Formula

ΔP=K⋅ρv22\Delta P = K \cdot \frac{\rho v^2}{2}

Calculator

Notes

  • Results are approximate and should be verified for critical applications
  • Input values should be within reasonable engineering ranges

Pressure Loss Due to Friction - Roughness Coefficients

8 rows
Table 1: Absolute roughness coefficients for common pipe and duct materials
Surface Material
Absolute Roughness k (10⁻³ m)
Absolute Roughness k (feet)
Copper, Lead, Brass, Aluminum (new)0.001 - 0.0023.3 - 6.7×10⁻⁶
PVC & Plastic Pipes0.0015 - 0.0070.5 - 2.33×10⁻⁵
Epoxy, Vinyl Ester & Isophthalic pipe0.0051.7×10⁻⁵
Stainless steel, bead blasted0.001 - 0.006(0.00328 - 0.0197) × 10⁻³
Stainless steel, turned0.0004 - 0.006(0.00131 - 0.0197) × 10⁻³
Stainless steel, electropolished0.0001 - 0.0008(0.000328 - 0.00262) × 10⁻³
Steel commercial pipe0.045 - 0.091.5 - 3×10⁻⁴
Stretched steel0.0155×10⁻⁵

Source: engineeringtoolbox.com

Energy Equation

The total energy per mass unit in a fluid flow consists of elevation (potential) energy, velocity (kinetic) energy, and pressure energy. The Energy Equation states that energy cannot disappear—the energy upstream equals the energy downstream plus the energy loss:

E1=E2+ElossE_1 = E_2 + E_{loss}

Where the energy in a specific point in the flow is:

Eflow=Epressure+Ekinetic+EpotentialE_{flow} = E_{pressure} + E_{kinetic} + E_{potential}

The components are defined as:

Energy ComponentFormula
Pressure energyEpressure=pρE_{pressure} = \frac{p}{\rho}
Kinetic energyEkinetic=v22E_{kinetic} = \frac{v^2}{2}
Potential energyEpotential=ghE_{potential} = gh
Energy lossEloss=ΔplossρE_{loss} = \frac{\Delta p_{loss}}{\rho}

For two points in a stream line, combining these gives the general energy equation:

p1ρ+v122+gh1=p2ρ+v222+gh2+Δplossρ\frac{p_1}{\rho} + \frac{v_1^2}{2} + gh_1 = \frac{p_2}{\rho} + \frac{v_2^2}{2} + gh_2 + \frac{\Delta p_{loss}}{\rho}

Minor (Dynamic) Pressure Loss

The minor or dynamic loss depends on flow velocity, fluid density, and a loss coefficient for the specific component:

Δpminor_loss=ξρv22\Delta p_{minor\_loss} = \xi \frac{\rho v^2}{2}

Where ξ\xi is the minor loss coefficient (dimensionless), specific to each type of fitting, valve, or bend.

Head and Head Loss Equations

The energy equation can be expressed in terms of head by dividing each term by the specific weight γ=ρg\gamma = \rho g:

p1γ+v122g+h1=p2γ+v222g+h2+Δhloss\frac{p_1}{\gamma} + \frac{v_1^2}{2g} + h_1 = \frac{p_2}{\gamma} + \frac{v_2^2}{2g} + h_2 + \Delta h_{loss}

The major friction head loss is:

Δhmajor_loss=λldhv22g\Delta h_{major\_loss} = \lambda \frac{l}{d_h} \frac{v^2}{2g}

The minor dynamic head loss is:

Δhminor_loss=ξv22g\Delta h_{minor\_loss} = \xi \frac{v^2}{2g}

Friction Coefficient

The friction coefficient λ\lambda depends on the flow regime and pipe roughness.

Laminar Flow

For fully developed laminar flow (Re<2300Re < 2300), roughness can be neglected:

λ=64Re\lambda = \frac{64}{Re}

Turbulent Flow

For turbulent flow, the friction coefficient depends on both Reynolds number and relative roughness:

λ=f(Re,kdh)\lambda = f\left(Re, \frac{k}{d_h}\right)

Flow Regime Classification

The flow regime is determined by the Reynolds number ReRe:

RegimeCondition
LaminarRe<2300Re < 2300
Transient2300<Re<40002300 < Re < 4000
TurbulentRe>4000Re > 4000

In the transient zone, the flow varies between laminar and turbulent, and the friction coefficient cannot be precisely determined.

References

Source: engineeringtoolbox.com