Pipeline Flow Rate Calculator

Pipeline Fluid Flow Rate Estimator

Input Fields

Hydraulic gradient

S

%

Kinematic viscosity of water

v

m²/s

Internal diameter

D

m

Roughness coefficient

Kₛ

m

Area of section

A

m²

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Your Results

Pipeline flow rate

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Pipeline Flow Rate Calculation Formula

$$Q = \frac{\pi D^2}{4} \cdot \frac{\sqrt{2gS}}{\sqrt{K_s / v}}$$

Where:

• $$Q$$ — flow rate (m³/s)
• $$D$$ — internal pipe diameter (m)
• $$g$$ — gravitational acceleration (9.81 m/s²)
• $$S$$ — slope (m/m or unitless gradient)
• $$K_s$$ — roughness coefficient (m)
• $$v$$ — kinematic viscosity (m²/s)

This formula approximates flow in partially full or full gravity-driven pipes, combining hydraulic principles and empirical roughness adjustments.

This formula is useful for estimating the discharge capacity of pipelines, especially in open channel or gravity flow conditions. Adjustments for pipe roughness $$K_s$$ and fluid viscosity $$v$$ improve accuracy for various fluid types and materials. Typical applications include drainage design, stormwater systems, and municipal water engineering. The calculator simplifies complex hydraulic computations into one quick result.