Question

The flow of glycerin (kinematic viscosity $v=5\times {10}^{-4}{m}^2/s$) in an open channel is to be modeled in a laboratory flume using water $(v={10}^{-6}{m}^2/s)$ as the flowing fluid. If both gravity and viscosity are important, what should be the length scale (i.e ratio of prototype to model dimensions) for maintaining dynamic similarity?

• A. 1
• B. 22
• C. 63
• D. 500

Answer 1

The correct option is C 63

Equating Reynolds number and Froude number, we get
$\frac{V_r{L}_r}{{\nu }_r}=\frac{V_r}{\sqrt{L_r}}$
$\therefore L_r=({\nu }_r{)}^{2/3}$
${\nu }_r=\frac{{\nu }_m}{{\nu }_p}=\frac{{10}^{-6}}{5\times {10}^{-4}}=2\times {10}^{-3}$
$\Rightarrow L_r=(2\times {10}^{-3}{)}^{2/3}$
$\Rightarrow L_r=0.0159$
$But{L}_r=\frac{L_m}{L_p}$

$\Rightarrow \frac{L_p}{L_m}=\frac{1}{L_r}=\frac{1}{0.0159}=62.99=63$