How to use this calculator
Choose open or differential. Enter the densities of the fluids and the vertical heights shown in the sketch: from each pipe down to the gauge-fluid meniscus on its side, and the difference in the gauge-fluid levels.
Formulas
The walkstart at A, add ρgh going down, subtract going up, end at B
DifferentialpA − pB = ρmgΔh + ρBg hB − ρAg hA
Worked example
Water pipes A and B, mercury reading 15 cm, A 30 cm and B 10 cm above their menisci (the default)
- ρmgΔh = 13 600 × 9.81 × 0.15 = 20 012 Pa.
- ρBghB = 981 Pa and ρAghA = 2943 Pa.
- pA − pB = 20 012 + 981 − 2943 = 18.05 kPa.
Frequently asked questions
Which way do I add and subtract?
Going down through a fluid the pressure rises by ρgh; going up it falls. Across a horizontal line in one continuous fluid the pressure is the same.
Why use mercury?
It is 13.6 times denser than water, so a large pressure gives a short, readable column.