FLD-22

Darcy friction pressure drop

Δp = f (L/D) (ρ v² / 2). The Darcy–Weisbach pipe formula in pascals.

Reading speed

FluidsDarcy

Governing equation

\Delta p=f\dfrac{L}{D}\dfrac{\rho v^2}{2}

$v \in \left[0.1, 12\right]$

where

f: Friction factor (—)
L: Length (m)
D: Diameter (m)
\rho: Density (kg/m³)
v: Speed (m/s)
\Delta p: Pressure drop (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

\Delta p=f\dfrac{L}{D}\dfrac{\rho v^2}{2}

$v \in \left[0.1, 12\right]$

$v = 0.1$ $\Delta p = 0.04$

Along the curve

②

Domain of the variable — blue

v_{\min} = 0.1,\quad v_{\max} = 12

$v \in \left[0.1, 12\right]$

$v = 0.1$ $v = 0.1$

Along the curve

③

Response curve — green

\Delta p=f\dfrac{L}{D}\dfrac{\rho v^2}{2}

$v \in \left[0.1, 12\right]$

$v = 0.1$ $\Delta p = 0.04$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta p}{\mathrm{d}v}

$v \in \left[0.1, 12\right]$

$v = 0.175$ $\Delta p^{\prime} = 1.399$

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-22 — Darcy friction pressure drop) is the form associated with Darcy. Working symbols: $f$ , $L$ , $D$ , $\rho$ , $v$ $\rightarrow$ $\Delta p$ . Laminar f = 64/Re. Turbulent f from Moody, a function of Re and ε/D.

Purpose

Purpose: compute

\Delta p

from

f

L

D

\rho

v

in Fluid physics via

\Delta p=f\dfrac{L}{D}\dfrac{\rho v^2}{2}

Δp = f (L/D) (ρ v² / 2). The Darcy–Weisbach pipe formula in pascals. 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

f = 0.020\,\mathrm{—}

L = 80.000\,\mathrm{m}

D = 0.200\,\mathrm{m}

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

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

, the governing relation

\Delta p=f\dfrac{L}{D}\dfrac{\rho v^2}{2}

yields

\Delta p = 16.00\,\mathrm{kPa}

. A long pipe, wall roughness, a falling p. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Friction factor f0.02 —Length L80 mDiameter D0.2 mDensity \rho1000 kg/m³Speed v2 m/s

Outputs

Pressure drop \Delta p16.00 kPa

Reading speed

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Narration of this film

A long pipe, wall roughness, a falling p.

Laminar f = 64/Re. Turbulent f from Moody, a function of Re and ε/D.

Reading speed

Watch on YouTube