PLAIN AND CIVIL: EXAMPLE 6.4.3. HYDRAULIC RADIUS FOR PIPES FLOWING LESS THAN HALF FULL

Calculate the hydraulic radius (m) for water flowing 20 mm deep in a pipe of 100 mm diameter.

Solve for the angle $\theta$ : [setting your calculator at Radians mode]

$\theta =2cos^{-1}\left ( \frac{r-h}{r} \right )$

$\theta =2cos^{-1}\left ( \frac{50mm-20mm}{50mm} \right )=1.8546$

Then proceed with solving the area and wetted perimeter:

$A=\frac{r^{2}\left ( \theta -sin\theta \right )}{2}$

$A=\frac{0.050^{2}\left ( 1.8546 -sin1.8546 \right )}{2}=1.1183x10^{-3}m^{2}$

And,

$P=r\theta =0.05\left ( 1.8546 \right )=0.09273m$

So the hydraulic radius becomes:

$R=\frac{A}{P}=\frac{1.1183x10^{-3}}{0.09273}$

${\color{Red} \mathbf{R=0.01206m}}$

RELATED TOPIC:

6.4. THE HYDRAULIC RADIUS

PLAIN AND CIVIL

Pages

Monday, 22 April 2019

EXAMPLE 6.4.3. HYDRAULIC RADIUS FOR PIPES FLOWING LESS THAN HALF FULL

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