The shear stress due to the viscosity of the fluid and the friction force at the pipe wall create a resistance to flow, expressed as a pressure loss and expressed in meters (of pipe).
The calculation is done with the Darcy-Weisbach/Colebrook formula, which has the following form:

• h: load drop [m]
• f: friction factor (dimensionless, depends on surface roughness and flow regime
• L: flow length [m]
• v: flow velocity [m/s]
• d: flow diameter (inner diameter of the pipe) [m]
• g: gravitational acceleration [m/s²]

Flow velocity [m/s] is calculated from the flow rate and the flow section

• Q: flow rate [m³/s]
• d: flow diameter (inner diameter of the pipe) [m]

The friction factor is dependent on the flow regime: laminar (Re≤2000), turbulent (Re≥4,000) or transient.

The flow regime is determined by the Reynolds number:

• Re: Reynolds number, dimensionless
• ρ: density [kg/m³]”
• v: flow velocity [m/s]
• d: flow diameter (inner diameter of the pipe) [m]
• eta: dynamic viscosity [kg/m×s]

Dynamic viscosity (η) is a property of a fluid, measured in [kg/m*s] and is temperature dependent.

For laminar regime:

For turbulent regime (Colebrook formula):

• ε: roughness [m]
• Re: Reynolds number, dimensionless

Some typical roughness values ​​[m] for the main materials used in pipe construction:

For transient regimes, the Darcy friction factor cannot be calculated with acceptable accuracy and the algorithm does not apply.

Note: Pressure loss [kg/m×s or Pa] is calculated from the pressure loss with the formula: Δp = ρgh

• ρ: density, [kg/m³]
• g: gravitational acceleration. [m/s²]
• h: load loss. [m]