FLD-13

Lift force

L = ½ ρ v² S C_L. The aerodynamic lift equation.

Reading speed

FluidsLift

Governing equation

L=\tfrac12\rho v^2 S C_L

$v \in \left[5, 300\right]$

where

\rho: Density (kg/m³)
v: Speed (m/s)
S: Area (m²)
C_L: Lift coefficient (—)
L: Lift (kN)

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

L=\tfrac12\rho v^2 S C_L

$v \in \left[5, 300\right]$

$v = 5$ $L = 0.196$

Along the curve

②

Domain of the variable — blue

v_{\min} = 5,\quad v_{\max} = 300

$v \in \left[5, 300\right]$

$v = 5$ $v = 5$

Along the curve

③

Response curve — green

L=\tfrac12\rho v^2 S C_L

$v \in \left[5, 300\right]$

$v = 5$ $L = 0.196$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}L}{\mathrm{d}v}

$v \in \left[5, 300\right]$

$v = 6.855$ $L^{\prime} = 0.107$

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-13 — Lift force) is the form associated with Lift. Working symbols: $\rho$ , $v$ , $S$ , $C_L$ $\rightarrow$ $L$ . C_L grows with angle of attack until stall. Circulation theorem of Kutta–Joukowski.

Purpose

Purpose: compute

L

from

\rho

v

S

C_L

in Fluid physics via

L=\tfrac12\rho v^2 S C_L

L = ½ ρ v² S C_L. The aerodynamic lift equation. 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 = 60.000\,\mathrm{m/s}

S = 16.000\,\mathrm{m^{2}}

C_L = 0.800\,\mathrm{—}

, the governing relation

L=\tfrac12\rho v^2 S C_L

yields

L = 28.22\,\mathrm{kN}

. A wing, a circulation, an upward arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Density \rho1.225 kg/m³Speed v60 m/sArea S16 m²Lift coefficient C_L0.8 —

Outputs

Lift L28.22 kN

Reading speed

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Narration of this film

A wing, a circulation, an upward arrow.

C_L grows with angle of attack until stall. Circulation theorem of Kutta–Joukowski.

Reading speed

Watch on YouTube