Pipe Pressure Drop Calculator

The Pipe Pressure Drop Calculator computes the head loss and pressure drop for water flowing through a pipe run. It works out the velocity and Reynolds number, identifies the flow regime, finds the Darcy friction factor from the Colebrook equation, and reports the friction loss along the straight pipe, the loss across the fittings and valves you list, and the total as both head and pressure.

It also reports the same friction loss computed by Hazen-Williams, so you can compare the two methods on identical inputs.

It works in SI units: millimetres for diameter, metres for length and head, litres per second for flow, degrees Celsius for temperature and kilopascals for pressure.

Use it to check a liquid pipe run carrying water. It models one pipe under steady flow.

Purpose and model boundary

This model calculates velocity, Reynolds number, Darcy friction factor, major and minor head loss, and pressure drop for water in one constant-diameter pipe run. It also reports Hazen-Williams head loss as a comparison and generates a system-loss curve over flow. It supports hydraulic diagnostics and preliminary sizing checks; it does not solve a network, include static elevation head, select a pump, model compressible or non-Newtonian flow, or replace a transient/surge analysis.

Inputs and units

Flow is entered in L/s, internal diameter in mm, and pipe length in m. Water temperature selects a workbook row containing density in kg/m³ and kinematic viscosity in m²/s. Pipe material selects an illustrative absolute roughness in mm. Counts are supplied for long-radius and standard 90° elbows, through and branch tees, open gate and globe valves, and check valves. Hazenwilliams is the comparison coefficient C.

Governing relationships

After converting Q to m³/s and D to m:

A = pi × D² / 4

V = Q / A

Re = V × D / nu

relative roughness = epsilon / D

For turbulent flow the workbook seeds the Darcy friction factor with Swamee-Jain:

f_0 = 0.25 / [log10(epsilon/(3.7D) + 5.74/Re^0.9)]²

It then performs six explicit Colebrook fixed-point refinements:

f_(k+1) = 1 / [-2 log10(epsilon/(3.7D) + 2.51/(Re sqrt(f_k)))]²

For Re < 2300, it instead uses f = 64/Re. Fitting loss coefficient is K_total = sum(count_j × K_j). Head losses are:

h_major = f × (L/D) × V²/(2g)

h_minor = K_total × V²/(2g)

h_total = h_major + h_minor

pressure drop = density × g × h_total / 1000 kPa

The comparison relationship is h_HW = 10.67 × L × Q^1.852 / (C^1.852 × D^4.87) using SI inputs.

Calculation sequence

1. Convert units and look up water density/viscosity and material roughness.
2. Calculate area, velocity, Reynolds number, and relative roughness.
3. Use laminar 64/Re below 2300; otherwise use the Swamee-Jain seed followed by six Colebrook refinements.
4. Sum fitting counts times the workbook's illustrative K values.
5. Calculate major, minor, and total head loss, then convert total head to kPa and kPa per 100 m.
6. Calculate Hazen-Williams head loss independently for comparison.
7. Repeat the hydraulic loss calculation over the chart's flow points and evaluate status.

Outputs and interpretation

Total_Head_Loss and Pressure_Drop are the primary results. Supporting outputs show pressure drop per 100 m, velocity, Reynolds number, flow regime, relative roughness, Darcy friction factor, the major/minor split, and Hazen-Williams head loss. The chart is the current pipe's total-loss curve; it should rise steeply as flow increases.

Validation and status logic

The transition warning takes precedence over the high-velocity warning. The flow-regime label is No flow, Laminar, Transitional, or Turbulent using the same Reynolds thresholds.

Assumptions and limitations

• The fluid is water at one of six stored temperatures. Density and viscosity are illustrative lookup values; interpolation is not performed.
• The pipe has constant circular diameter, steady fully developed flow, and one selected absolute roughness. Ageing, fouling, entrance effects, fittings not listed, and distributed diameter changes are excluded.
• K coefficients are illustrative constants independent of Reynolds number and fitting geometry.
• The Colebrook calculation is unrolled into a seed plus six refinements; it is not an iterative workbook setting. The workbook audit states agreement with a converged turbulent root to better than 1e-6 over its tested turbulent domain.
• In the transition region, the workbook still returns a calculated friction value but flags uncertainty.
• Hazen-Williams is an empirical water-only comparison and is expected to differ from Darcy-Weisbach, especially for rough pipe and temperature changes.
• Static elevation, pump or turbine head, pressure-dependent properties, cavitation, water hammer, and network balancing are not included.

Restrictions and non-computing states

This calculator accepts only the six declared material and temperature choices and rejects negative flow, diameter, length, and fitting counts. Flow, diameter, and length must also be strictly positive in the workbook. Hazenwilliams may be zero: the protected comparison then returns zero while the Darcy result remains available. Counts are whole numbers. The page cannot edit the embedded density, viscosity, roughness, K, or gravity tables.

Errors and warnings

An invalid dropdown, grid shape, or value outside its allowed range is rejected before calculation. Workbook NOT VALID means the core Darcy basis lacks positive flow, diameter, or length. Workbook CHECK preserves the calculation but flags transition-regime uncertainty or excessive velocity. A connection or calculation-service failure is a service error and must not be interpreted as zero loss.

The workbook derives its relations rather than reproducing any table, chart or figure from a standard or agency publication. The friction factor is solved from the Colebrook equation, and the Hazen-Williams comparison uses the standard empirical form.

• Wikipedia. Darcy-Weisbach equation. https://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation
• Wikipedia. Colebrook equation and the Moody chart it underlies. https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae
• Wikipedia. Hazen-Williams equation, including its restriction to water in the turbulent regime. https://en.wikipedia.org/wiki/Hazen%E2%80%93Williams_equation
• Wikipedia. Minor losses in pipe flow. https://en.wikipedia.org/wiki/Minor_losses_in_pipe_flow

Absolute roughness values, Hazen-Williams coefficients and minor-loss coefficients shipped with the workbook are typical published values and carry no authority. Values for design should come from the pipe and component manufacturers, and should allow for ageing.

Additional source notes migrated from Methodology

The workbook uses Darcy-Weisbach, Colebrook-White with a Swamee-Jain starting estimate, the K-factor minor-loss method, and Hazen-Williams for comparison. The reviewer packet cites Engineering ToolBox on Darcy-Weisbach, Engineering ToolBox on Hazen-Williams, and Best-Calculators' friction-loss comparison.