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Hydraulic Head Difference & Gradient

Find the signed head drop per unit distance between two points sharing a hydraulic-head datum.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Heads of 12 m and 10 m separated by 20 m give a head drop of 2 m and a dimensionless gradient of 0.1 in the point-1-to-point-2 direction.

Head drop = h₁ − h₂; hydraulic gradient = (h₁ − h₂) / separation

Worked example

Enter these known values and leave the other values blank.

Hydraulic head at point 1
12 m
Hydraulic head at point 2
10 m
Positive separation distance
20 m
Signed head drop from point 1 to point 2
2 m
Signed hydraulic gradient
0.1

Assumptions and limitations

  • Separation must be positive. The retained source domain requires positive individual heads; choose a consistent reference datum that makes both heads positive.
  • Head drop and gradient may be positive, zero or negative. Use the same hydraulic-head definition and datum at both points.
  • The gradient is a dimensionless head-per-distance ratio. Flow rate additionally requires a flow model and properties such as hydraulic conductivity and cross-sectional area.

Common questions

What does a negative gradient mean?

With this sign convention, point 2 has higher head than point 1. Swapping the point labels reverses the gradient sign.

Does adding the same datum offset change the result?

No. Adding the same amount to both heads leaves their difference and the gradient unchanged.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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