Hydraulic Gradient Calculator

What Is Hydraulic Gradient?

Hydraulic gradient measures how much hydraulic head drops over a given distance in a pipe, channel, or soil column. It is the slope of the energy grade line and drives flow in open channels and porous media. Engineers use it to compare friction losses, check pump head requirements, and size drainage systems.

How to Calculate Hydraulic Gradient

The hydraulic gradient $i$ is the ratio of head loss to length:

$$i = \frac{\Delta h}{L}$$

where $\Delta h$ is the head loss in meters and $L$ is the pipe or channel length in meters. The result is dimensionless but often reported as m/m. The slope angle $\theta$ relates to the gradient by $\theta = \arctan(i)$.

Frequently Asked Questions

What units does hydraulic gradient use?

Hydraulic gradient is dimensionless because head loss and length share the same unit. It is commonly expressed as m/m, ft/ft, or as a percentage (multiply by 100).

How is hydraulic gradient different from slope?

Channel bed slope is the physical incline of the bottom. Hydraulic gradient is the slope of the total energy line, which includes velocity head and friction losses.

What is a typical gradient in a pipe?

Gravity sewer lines often run at 0.5% to 2% (0.005 to 0.02 m/m). Steeper gradients increase flow velocity but may require energy dissipation structures downstream.

Can hydraulic gradient exceed 1?

Yes. A gradient of 1 means one meter of head loss per meter of length, equivalent to a 45° slope angle. Very steep gradients appear in short fittings or rapid flow transitions.

How does gradient relate to Darcy's law?

In groundwater flow, discharge velocity is proportional to hydraulic conductivity times hydraulic gradient: $v = K \times i$. Higher gradient drives more flow through the same porous medium.

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What Is Hydraulic Gradient?

How to Calculate Hydraulic Gradient

Frequently Asked Questions

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