Chapter 14, Problem 14.1PP

Compute the hydraulic radius for a circular drain pipe running half full if its inside diameter is $300$ mm.

To determine

The hydraulic radius for a circular drain pipe running half full.

Answer to Problem 14.1PP

The hydraulic radius for a circular drain pipe running half full is $R=75mm$

Explanation of Solution

Given Information:

Pipe diameter, $D=300mm$

Hydraulic radius,

   $R=\frac{A}{WP}$

Here, A = cross sectional area

WP = Wetted perimeter

Half cross sectional area is $A=\frac{\pi }{8}{D}^2$

   $\therefore A=\frac{\pi }{8}{\left(300\right)}^2$

   $A=35342.92m{m}^2$

Wetted perimeter is given by,

   $WP=\frac{\pi }{2}D$

   $WP=\frac{\pi }{2}\left(300\right)$

   $WP=471.24mm$

We know,

   $R=\frac{A}{WP}$

   $\therefore R=\frac{35342.92}{471.24}$

   $R=75mm$

Conclusion:

The hydraulic radius for a circular drain pipe running half full is $R=75mm$