FLD-21

Blasius skin friction

c_f = 0.664 / √Re_x on a laminar flat plate. Local skin-friction coefficient.

Reading speed

FluidsBlasius

Governing equation

c_f=0.664/\sqrt{Re_x},\quad Re_x=U x/\nu

$x \in \left[0.01, 10\right]$

where

U: Free speed (m/s)
x: Distance (m)
\nu: Kinematic viscosity (mm²/s)
Re_x: Local Reynolds (—)
c_f: Skin friction (—)
\delta: Thickness (mm)

The figure, part by part

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①

Governing law — red

c_f=0.664/\sqrt{Re_x},\quad Re_x=U x/\nu

$x \in \left[0.01, 10\right]$

$x = 0.01$ $Re_x = 0.008$

Along the curve

②

Domain of the variable — blue

x_{\min} = 0.01,\quad x_{\max} = 10

$x \in \left[0.01, 10\right]$

$x = 0.01$ $x = 0.01$

Along the curve

③

Response curve — green

c_f=0.664/\sqrt{Re_x},\quad Re_x=U x/\nu

$x \in \left[0.01, 10\right]$

$x = 0.01$ $Re_x = 0.008$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Re_x}{\mathrm{d}x}

$x \in \left[0.01, 10\right]$

$x = 0.073$ $Re_x^{\prime} = -0.047$

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-21 — Blasius skin friction) is the form associated with Blasius. Working symbols: $U$ , $x$ , $\nu$ $\rightarrow$ $Re_x$ , $c_f$ , $\delta$ . Blasius solved the similar boundary layer. Thickness δ ≈ 5 x / √Re_x.

Purpose

Purpose: compute

Re_x

c_f

\delta

from

U

x

\nu

in Fluid physics via

c_f=0.664/\sqrt{Re_x},\quad Re_x=U x/\nu

c_f = 0.664 / √Re_x on a laminar flat plate. Local skin-friction coefficient. 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

U = 10.000\,\mathrm{m/s}

x = 0.500\,\mathrm{m}

\nu = 15.000\,\mathrm{mm^{2}/s}

, the governing relation

c_f=0.664/\sqrt{Re_x},\quad Re_x=U x/\nu

yields

Re_x = 333333\,\mathrm{—}

c_f = 0.00115\,\mathrm{—}

\delta = 4.33\,\mathrm{mm}

. A plate, a growing layer, a wall shear. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Free speed U10 m/sDistance x0.5 mKinematic viscosity \nu15 mm²/s

Outputs

Local Reynolds Re_x333333 —
Skin friction c_f0.00115 —
Thickness \delta4.33 mm

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Narration of this film

A plate, a growing layer, a wall shear.

Blasius solved the similar boundary layer. Thickness δ ≈ 5 x / √Re_x.

Reading speed

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