CHE-40

Dittus–Boelter Nu

Turbulent pipe Nusselt.

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GoverningDittus–Boelter Nu

Governing equation

Nu=0.023 Re^{0.8} Pr^{n}

$Re \in \left[4000, 2\times 10^{5}\right]$

where

Re: Re (—)
Pr: Pr (—)
n: n (—)
Nu: Dittus–Boelter Nu (—)

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

Nu=0.023 Re^{0.8} Pr^{n}

$Re \in \left[4000, 2\times 10^{5}\right]$

$Re = 4000$ $Nu = 38.14$

Along the curve

②

Domain of the variable — blue

Re_{\min} = 4000,\quad Re_{\max} = 2\times 10^{5}

$Re \in \left[4000, 2\times 10^{5}\right]$

$Re = 4000$ $Re = 4000$

Along the curve

③

Response curve — green

Nu=0.023 Re^{0.8} Pr^{n}

$Re \in \left[4000, 2\times 10^{5}\right]$

$Re = 4000$ $Nu = 38.14$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Nu}{\mathrm{d}Re}

$Re \in \left[4000, 2\times 10^{5}\right]$

$Re = 5232.7$ $Nu^{\prime} = 0.007$

Along the curve

Lecture brief

Historical brief

From CSTR/PFR mole balances and Arrhenius rates to McCabe–Thiele stages and NTU exchangers, chemical engineering is conservation plus equilibrium. The lab is that design arithmetic. This sheet (CHE-40 — Dittus–Boelter Nu) is the form associated with Dittus–Boelter Nu. Working symbols: $Re$ , $Pr$ , $n$ $\rightarrow$ $Nu$ . Turbulent pipe Nusselt. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

Nu

from

Re

Pr

n

in Chemical engineering via

Nu=0.023 Re^{0.8} Pr^{n}

Turbulent pipe Nusselt. Use it when a real chemical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Re = 20000.000\,\mathrm{—}

Pr = 7.000\,\mathrm{—}

n = 0.400\,\mathrm{—}

, the governing relation

Nu=0.023 Re^{0.8} Pr^{n}

yields

Nu = 138.226\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Re Re20000 —Pr Pr7 —n n0.4 —

Outputs

Dittus–Boelter Nu Nu138.226 —

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Turbulent pipe Nusselt. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube