Hydrostatic Pressure: Formulas, Devices, and Manometer Methods

Hydrostatic pressure at any point in a liquid column equals the product of the liquid’s unit weight (γ) and the vertical distance (head, h) from the free surface:

[ P = \gamma \times h ]

The unit weight of water is 9.81 kN/m³, and the same relationship holds for any fluid when its specific gravity (SG) is accounted for.

Measurement Devices

Non‑Borden tube gauge – the common industrial pressure gauge that reads pressure directly from the fluid column.

Piezometer – a vertical tube attached to a container or pipe; the internal pressure forces the liquid inside the tube to rise, and the height increase directly indicates pressure.

U‑tube manometer – a U‑shaped tube filled with a liquid (often mercury). Pressure differences create a differential head, or “head loss,” between the two arms, allowing the pressure to be calculated from the height difference.

“Two points have the same pressure when they are on the same level or on the same elevation.”

Manometer Calculation Methodology

1. Convert all liquid heads to equivalent water heads. Use the specific‑gravity ratio:

[ h_{\text{water}} = h_{\text{fluid}} \times \frac{SG_{\text{fluid}}}{1} ]

For mercury (SG = 13.6), benzene (SG = 0.80), and kerosene (SG = 0.82), the conversion scales each head to a water‑equivalent value.

1. Identify fluid interfaces as primary calculation points. Begin at one end of the system and move through each interface.

2. Apply the equal‑pressure principle: points at the same elevation within the same continuous fluid have equal pressure.

3. Follow directional rules while traversing the system: moving downward adds pressure, moving upward subtracts pressure.

“If we go down we add pressure but if we go up we subtract pressure.”

1. Sum the pressure heads from the starting point to the target point, accounting for each conversion and elevation change. The final sum equals the pressure at the target point (or zero if the point is exposed to free air).

Worked Examples

Example 1 – A three‑fluid column (water, benzene, mercury) yields a pressure difference of 13.734 kPa after converting each head to water equivalents and applying the directional rules.

Example 2 – A similar setup with kerosene instead of benzene produces a pressure difference of 10.323 kPa.

Example 3 (Piezometer) – Elevations at points E, F, and G are 12.51 m, 12.357 m, and 10.72 m respectively. Mercury deflection of 0.614 m translates to the pressure indicated by the piezometer.

These examples illustrate the systematic approach: convert, track interfaces, apply equal‑pressure and directional rules, and sum the heads to obtain the desired pressure.