FLD-14

Drag force

D = ½ ρ v² S C_D. Quadratic drag on a bluff or streamlined body.

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FluidsDrag

Governing equation

D=\tfrac12\rho v^2 S C_D

$v \in \left[0.5, 80\right]$

where

\rho: Density (kg/m³)
v: Speed (m/s)
S: Area (m²)
C_D: Drag coefficient (—)
D: Drag (N)

The figure, part by part

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①

Governing law — red

D=\tfrac12\rho v^2 S C_D

$v \in \left[0.5, 80\right]$

$v = 0.5$ $D = 0.028$

Along the curve

②

Domain of the variable — blue

v_{\min} = 0.5,\quad v_{\max} = 80

$v \in \left[0.5, 80\right]$

$v = 0.5$ $v = 0.5$

Along the curve

③

Response curve — green

D=\tfrac12\rho v^2 S C_D

$v \in \left[0.5, 80\right]$

$v = 0.5$ $D = 0.028$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}D}{\mathrm{d}v}

$v \in \left[0.5, 80\right]$

$v = 1$ $D^{\prime} = 0.221$

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-14 — Drag force) is the form associated with Drag. Working symbols: $\rho$ , $v$ , $S$ , $C_D$ $\rightarrow$ $D$ . C_D is a function of Re and shape. A sphere sits near 0.47; a foil near 0.01.

Purpose

Purpose: compute

D

from

\rho

v

S

C_D

in Fluid physics via

D=\tfrac12\rho v^2 S C_D

D = ½ ρ v² S C_D. Quadratic drag on a bluff or streamlined body. 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 = 1.225\,\mathrm{kg/m^{3}}

v = 25.000\,\mathrm{m/s}

S = 0.600\,\mathrm{m^{2}}

C_D = 0.300\,\mathrm{—}

, the governing relation

D=\tfrac12\rho v^2 S C_D

yields

D = 68.91\,\mathrm{N}

. A body, a wake, a backward arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Density \rho1.225 kg/m³Speed v25 m/sArea S0.6 m²Drag coefficient C_D0.3 —

Outputs

Drag D68.91 N

Reading speed

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Narration of this film

A body, a wake, a backward arrow.

C_D is a function of Re and shape. A sphere sits near 0.47; a foil near 0.01.

Reading speed

Watch on YouTube