FLD-01

Bernoulli head

p/ρg + v²/2g + z = H along a streamline of an ideal fluid.

Reading speed

FluidsBernoulli

Governing equation

H=\dfrac{p}{\rho g}+\dfrac{v^2}{2g}+z

$v \in \left[0, 20\right]$

where

p: Pressure (kPa)
v: Speed (m/s)
z: Elevation (m)
\rho: Density (kg/m³)
H: Total head (m)

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

H=\dfrac{p}{\rho g}+\dfrac{v^2}{2g}+z

$v \in \left[0, 20\right]$

$v = 0$ $H = 17.23$

Along the curve

②

Domain of the variable — blue

v_{\min} = 0,\quad v_{\max} = 20

$v \in \left[0, 20\right]$

$v = 0$ $v = 0$

Along the curve

③

Response curve — green

H=\dfrac{p}{\rho g}+\dfrac{v^2}{2g}+z

$v \in \left[0, 20\right]$

$v = 0$ $H = 17.23$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}H}{\mathrm{d}v}

$v \in \left[0, 20\right]$

$v = 0.126$ $H^{\prime} = 0.013$

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-01 — Bernoulli head) is the form associated with Bernoulli. Working symbols: $p$ , $v$ , $z$ , $\rho$ $\rightarrow$ $H$ . Steady, incompressible, inviscid, along a streamline. Viscosity needs Bernoulli-with-losses.

Purpose

Purpose: compute

H

from

p

v

z

\rho

in Fluid physics via

H=\dfrac{p}{\rho g}+\dfrac{v^2}{2g}+z

p/ρg + v²/2g + z = H along a streamline of an ideal fluid. 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

p = 120.000\,\mathrm{kPa}

v = 2.000\,\mathrm{m/s}

z = 5.000\,\mathrm{m}

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

, the governing relation

H=\dfrac{p}{\rho g}+\dfrac{v^2}{2g}+z

yields

H = 17.436\,\mathrm{m}

. A pipe that narrows, a speed rise, a pressure drop. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Pressure p120 kPaSpeed v2 m/sElevation z5 mDensity \rho1000 kg/m³

Outputs

Total head H17.436 m

Reading speed

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Narration of this film

A pipe that narrows, a speed rise, a pressure drop.

Steady, incompressible, inviscid, along a streamline. Viscosity needs Bernoulli-with-losses.

Reading speed

Watch on YouTube