FLD-15

Hydrostatic pressure

p = ρ g h. Gauge pressure under a free surface.

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FluidsHydrostatics

Governing equation

p=\rho g h

$h \in \left[0.1, 200\right]$

where

\rho: Density (kg/m³)
h: Depth (m)
p: Gauge pressure (kPa)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

p=\rho g h

$h \in \left[0.1, 200\right]$

$h = 0.1$ $p = 0.981$

Along the curve

②

Domain of the variable — blue

h_{\min} = 0.1,\quad h_{\max} = 200

$h \in \left[0.1, 200\right]$

$h = 0.1$ $h = 0.1$

Along the curve

③

Response curve — green

p=\rho g h

$h \in \left[0.1, 200\right]$

$h = 0.1$ $p = 0.981$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}p}{\mathrm{d}h}

$h \in \left[0.1, 200\right]$

$h = 1.357$ $p^{\prime} = 9.81$

Along the curve

Lecture brief

Historical brief

Bernoulli, Navier–Stokes, Reynolds (1883) and Stokes drag made continuum flow a dimensionless craft. The sheets compute head, drag, Re and a pedagogical NS snapshot. This sheet (FLD-15 — Hydrostatic pressure) is the form associated with Hydrostatics. Working symbols: $\rho$ , $h$ $\rightarrow$ $p$ . Pascal's law plus gravity. Independent of container shape.

Purpose

Purpose: compute

p

from

\rho

h

in Fluid physics via

p=\rho g h

p = ρ g h. Gauge pressure under a free surface. Use it when a real fluid physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\rho = 1000.000\,\mathrm{kg/m^{3}}

h = 10.000\,\mathrm{m}

, the governing relation

p=\rho g h

yields

p = 98.10\,\mathrm{kPa}

. A column, a depth, a pressure. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Density \rho1000 kg/m³Depth h10 m

Outputs

Gauge pressure p98.10 kPa

Reading speed

Watch on YouTube

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Narration of this film

A column, a depth, a pressure.

Pascal's law plus gravity. Independent of container shape.

Reading speed

Watch on YouTube