Resistance Coefficient K and Equivalent Length Calculator

Minor Loss Coefficients and K Values for Pipe Fittings

Pressure loss in piping systems consists of:

• Major losses, caused by friction along straight pipe sections
• Minor losses, caused by fittings, valves, bends, contractions, and expansions

Minor losses are quantified using resistance coefficients (K values) obtained from experimental data and standardized tables.

The calculator includes K values for:

• 90° elbows, return bends, and mitre bends
• Standard elbows and tees
• Pipe entrances and exits
• Sudden and gradual enlargements and contractions
• Valves (gate, globe, ball, butterfly, check valves, etc.)

Each fitting introduces additional energy dissipation that must be accounted for in system design.

Head Loss Equations Used in Pipe Flow Analysis

The total head loss in a piping system is the sum of major and minor losses.

Major Head Loss (Darcy–Weisbach Equation)

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

Where:

• h_f = major head loss
• f = Darcy friction factor
• L = pipe length
• D = pipe diameter
• V = flow velocity
• g = gravitational acceleration

Minor Head Loss Equation

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

Where:

• h_m = Minor head loss
• K = Minor loss coefficient
• V = Flow velocity
• g = Acceleration due to gravity

Minor losses become significant in systems with many fittings or short pipe runs.

Sudden Enlargement and Contraction

Using the momentum, continuity, and Bernoulli equations, the resistance coefficient for sudden enlargement and sudden contraction can be expressed as a function of pipe diameters:

Sudden enlargement:

$K_1={(1-\frac{d_1^2}{d_2^2})}^2$

Sudden contraction:

$K_1={0.5(1-\frac{d_1^2}{d_2^2})}^{}$

• K₁ = resistance coefficient
• d₁ = smaller internal diameter
• d₂ = larger internal diameter

Using the diameter ratio:

$\beta =\frac{d_1}{d_2}$

the resistance coefficient can be written in simplified form.

Sudden enlargement:

$K_1={(1-\frac{{\beta }^2}{})}^2$

Sudden contraction:

$K_1={0.5(1-\frac{{\beta }^2}{})}^{}$

To express the resistance coefficient based on the larger pipe diameter, the following relation applies:

$K_2={\frac{K_1}{{\beta }^4}}^{}$

• K₁ = resistance coefficient based on smaller diameter
• K₂ = resistance coefficient based on larger diameter

Sudden Enlargement and Contraction

If the enlargement or contraction is gradual, the resistance depends on the angle of divergence or convergence.

For gradual enlargement, the Gibson coefficient (Cₑ) is used to account for different divergence angles.

If the angle of divergence exceeds 45°, the resistance coefficient approaches that of a sudden enlargement.

For gradual contraction, the contraction coefficient (C𝑐) based on Crane test data is applied for various convergence angles.

Using these coefficients, the resistance coefficient can be calculated as:

• Gradual enlargement:
• Gradual contraction:

The resistance coefficient can be expressed relative to either the smaller or larger pipe diameter, depending on the calculation basis.

Application to Reduced-Bore Valves

The equations for gradual enlargement and contraction can also be applied to reduced-bore straight-through valves, such as:

• Ball valves
• Gate valves

For these valves, the total resistance coefficient is calculated as the sum of the contraction and enlargement resistance coefficients.

FINAL NOTE

You can use this calculator to determine:

• Resistance coefficient K
• Equivalent length l/d
• Minor head losses for fittings and valves

These results can be directly used in conjunction with a pressure drop calculator to evaluate piping system efficiency and ensure accurate hydraulic design.