What is a hydraulic gradient (verhang)?

A hydraulic gradient, called “verhang” in Dutch, is a relative difference in height: the height difference between two points divided by the distance between them. It is expressed as a percentage or in millimetres per metre. The term is used for sewers, drains and watercourses, and in soil mechanics for flowing groundwater. For pipes and gutters, English usually just speaks of the fall or gradient.

Gradient or fall?

Dutch distinguishes “verval” from “verhang”. Verval is the absolute difference in water level between two places, for example 20 cm. Verhang is that difference per unit of length. A pipe that drops 20 cm over 40 metres has a gradient of 5 mm per metre, or 0.5%.

In sewers and drains

In gravity pipes the water flows only under its own weight, so the gradient determines how fast it flows. Too little, and dirt settles in the pipe; too much, and the water rushes off while solids are left behind.

In soil mechanics

For groundwater, the hydraulic gradient is the difference in hydraulic head between two points along the direction of flow, divided by the distance. The steeper the gradient, the faster water moves through the soil. When water flows upwards, for instance as seepage behind a dike or into an excavation, the critical hydraulic gradient can be reached. At that point the water pressure equals the soil stress: the effective stress between the grains disappears and the sand starts to float and flow with the water. This is also called quick condition or heave, and it can develop into piping.

Application

• Laying sewers and drains: work in mm per metre and calculate how much height you need over the full length. Start at the connection point (the lowest point) and work back.
• Excavations and dewatering: an engineer calculates the gradient to make sure the base of the excavation does not heave.
• Watercourses: the gradient of a ditch or river determines its flow velocity.

Tips and points of attention

• Check with a spirit level or laser: a gradient of a few millimetres per metre is invisible to the naked eye.
• No back-fall: a single sagging pipe where water runs backwards is enough to create a spot where dirt collects.
• Mind the connection level: if the public sewer connection is high, you may not have enough height for an adequate gradient. Find out before you start digging.
• “Boiling” sand in an excavation: stop digging and call in a geotechnical engineer.

Related terms

• Slope
• Groundwater seepage
• Piping
• Sewer
• Drainage
• Soil mechanics

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