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Fluid Dynamics

Drag Force

Quadratic drag estimates the magnitude of fluid resistance using relative speed, reference area, density, and a drag coefficient.

F_{D} = \frac{1}{2} C_{D} ρ A v^{2}

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Source & review

Difficulty

Intermediate

Read time

5 min

Prerequisites

Basic algebra, consistent units, and the stated model assumptions

Review statusNeeds review

Source

OpenStax, College Physics 2e, §5.2 (Paul Peter Urone and Roger Hinrichs)

OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.

Adapted from OpenFormulaGraph, under CC BY 4.0.

FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.

Definition

Understanding the core concept

Quadratic drag estimates the magnitude of fluid resistance using relative speed, reference area, density, and a drag coefficient. Its direction opposes the object’s velocity relative to the fluid.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$F_{D}$	Force (drag)	$N$
$C_{D}$	Drag Coefficient	$1$
$ρ$	Density (fluid)	$kg/ m^{3}$
$A$	Reference area for the stated drag coefficient	$m^{2}$
$v$	Speed relative to the fluid	$m/s$

Real-World Applications

Where this formula is used in practice

Aerodynamic resistance

Estimate drag using a suitable coefficient.

Fluid loading

Compare drag as relative speed changes.

Worked Example

Step-by-step calculation with real numbers

Problem

An object moves relative to air at 10 m/s. With drag coefficient 0.5, air density 1.2 kg/m³, and frontal area 2 m², find the drag magnitude.

Given

C_{D} = 0.5

ρ = 1.2 kg/ m^{3}

A = 2 m^{2}

v = 10 m/s

Solution

F_{D} = \frac{1}{2} C_{D} ρ A v^{2}

F_{D} = \frac{( 0.5 ) \cdot ( 1.2 kg/ m ^{3} ) \cdot ( 2 m ^{2} ) \cdot ( 10 m/s ) ^{2}}{2}

F_{D} = 60 N

Final Answer

F_{D} = 60 N

Formula Guide

Info

DifficultyIntermediate

Read Time5 min

PrerequisitesBasic algebra, consistent units, and the stated model assumptions

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

OpenStax, College Physics 2e, §5.2 (Paul Peter Urone and Roger Hinrichs)

OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.

Adapted from OpenFormulaGraph, under CC BY 4.0.

FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.

Assumptions

• Use a drag coefficient appropriate to the geometry, reference area, Reynolds number, and flow conditions.
• The coefficient is treated as constant for this calculation; quadratic drag is not universal at very low speeds.

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Drag Force

Aerodynamic resistance

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