---
title: "Drag on sphere at Re = 0.2"
subject: "Fluid Mechanics"
chapter: 9
key: "semester_3/fluid_mechanics:sphere-drag-low-reynolds"
source: https://www.bctengineer.com/q/semester_3/fluid_mechanics/sphere-drag-low-reynolds
site: BCT Engineering
---

# Drag on sphere at Re = 0.2

Fluid Mechanics · Chapter 9: Flow past through submerged bodies

- Asked in: 2079 Baisakh, 2+4 marks
- Video: [Drag Coefficient of a Sphere - Terminal Velocity Example Problem using Drag Coefficient Figure](https://www.youtube.com/watch?v=O2o-zE-YbyE) — Brian Bernard
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/fluid_mechanics/sphere-drag-low-reynolds
- Whole chapter: https://www.bctengineer.com/md/semester_3/fluid_mechanics/chapter-9

## Question

What is the expression for the drag on a sphere, when Re of the flow is 0.2? Prove that the coefficient of drag for sphere for this range of the Reynolds number is given by $C_D = 24/Re$, where Re is the Reynolds number.

## Short answer

For a sphere at Re=0.2 the drag follows Stokes' law: F_D = 3πμVd. The drag coefficient C_D = 3πμVd / (0.5ρV^2 * πd²/4) simplifies to 24/Re, and at Re=0.2 yields C_D = 120.

## Answer

At very low Reynolds number ($Re < 1$, creeping flow) inertia is negligible compared with viscous forces, and the drag on a sphere is given by Stokes' law:

$$
F_D = 3\pi\mu V d
$$

where $\mu$ is the dynamic viscosity, $V$ the velocity of the sphere relative to the fluid, and $d$ the diameter. This holds for $Re = \rho V d/\mu \lesssim 0.2$ to $1$.

#### Proof that $C_D = 24/Re$

By definition the drag coefficient is the drag divided by the dynamic pressure times the projected area:

$$
C_D = \frac{F_D}{\tfrac12\rho V^2 A},\qquad A = \frac{\pi d^2}{4}
$$

Substituting Stokes' drag:

$$
\begin{aligned}
C_D &= \frac{3\pi\mu V d}{\tfrac12\rho V^2\cdot\dfrac{\pi d^2}{4}} = \frac{3\pi\mu V d\times 8}{\rho V^2\pi d^2} \\
&= \frac{24\mu}{\rho V d} = \frac{24}{Re}
\end{aligned}
$$

Hence for $Re = 0.2$:

$$
C_D = \frac{24}{0.2} = 120
$$

**Result: $F_D = 3\pi\mu V d$ and $C_D = 24/Re$ for the Stokes range.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the drag on a sphere for Re < 1?
   A. F_D = 6 pi mu V d^2
   B. F_D = 1/2 rho V^2 A
   C. F_D = 24 mu V
   D. F_D = 3 pi mu V d
   Answer: D. Stokes' law applies when inertia is negligible. (Key point: Stokes' law)

2. How is CD defined?
   A. CD = F_D/(rho V A)
   B. CD = F_D/(1/2 rho V^2 d)
   C. CD = F_D/(1/2 rho V^2 A) with A = pi d^2/4
   D. CD = F_D/(mu V d)
   Answer: C. Drag over dynamic pressure times projected area. (Key point: CD definition)

3. Substituting Stokes' drag gives
   A. CD = 12/Re
   B. CD = 24/Re
   C. CD = 48/Re
   D. CD = 24 Re
   Answer: B. 3 pi mu V d x 8/(rho V^2 pi d^2) = 24 mu/(rho V d). (Key point: Result)

4. What is CD at Re = 0.2?
   A. 120
   B. 4.8
   C. 24
   D. 0.0083
   Answer: A. CD = 24/0.2 = 120. (Key point: Value at Re = 0.2)

## Related in Fluid Mechanics

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