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Manometer Equation Calculator

Calculates the pressure difference between two points in a static fluid.

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Pressure Difference

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Overview

The manometer equation quantifies the pressure difference between two points in a static, incompressible fluid column based on its vertical height and density. It is derived from the principle of hydrostatic equilibrium, where the pressure at any depth is determined by the weight of the fluid column directly above it.

Symbols

Variables

- = Pressure Difference, = Fluid Density, g = Gravitational Acceleration, h = Height Difference

Pressure Difference
Pa
Fluid Density
Gravitational Acceleration
Height Difference

Apply it well

When To Use

When to use: Apply this formula when analyzing static fluids in U-tubes, tanks, or piezometers where the fluid is at rest and incompressible. It assumes a constant density throughout the column and that gravity is the only significant force acting on the fluid.

Why it matters: This relationship is fundamental for measuring pressure differences in industrial pipelines, monitoring gas flow in HVAC systems, and assessing atmospheric pressure. It provides a reliable mechanical method for pressure measurement that does not require complex electronic sensors.

Avoid these traps

Common Mistakes

  • Neglecting the gravitational constant (g ≈ 9.81 m/s²).
  • Using horizontal distance instead of vertical height difference.
  • Mixing units, such as using density in g/cm³ with height in meters.

One free problem

Practice Problem

A U-tube manometer uses mercury (density 13600 kg/m³) to measure the pressure difference between two points in a pipe. If the observed height difference between the mercury columns is 0.15 meters and gravity is 9.81 m/s², what is the pressure difference in Pascals?

Fluid Density13600 kg/m^3
Gravitational Acceleration9.81 m/s^2
Height Difference0.15 m

Solve for: deltaP

Hint: Multiply the fluid density by the gravitational constant and the vertical height difference.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Bird, Stewart, Lightfoot - Transport Phenomena
  2. Halliday, Resnick, Walker - Fundamentals of Physics
  3. Incropera, DeWitt, Bergman, Lavine - Fundamentals of Heat and Mass Transfer
  4. Wikipedia: Hydrostatic pressure
  5. Bird-Stewart-Lightfoot
  6. Incropera
  7. NIST Guide for the Use of the International System of Units (SI)
  8. Wikipedia: Hydrostatics