A circular sewer and a rectangular sewer are hydraulically equivalent. Find relation between depth of rectangular sewer and diameter of circular sewer if width of rectangular sewer is 2.5 times depth. Assume that only three sides of rectangular sewer are wetted.

Solution:

Let `b` and `d` be the width and depth of rectangular sewer and `D` be the diameter of circular sewer.

Here, width of rectangular sewer is, `b=2.5 d`

For hydraulically equivalent sewers, discharge in both are same,

`Q_R=Q_C`

or, `bd**1/n **((bd)/(b+2d))^(2/3)**(s)^(1/2)=(piD^2)/4**(d/4)^(2/3)**s^(1/2)`

Solving this equation for d, we get,

`d=0.531 D`

 Thus, the depth of rectangular sewer is 0.531 times the diameter of circular sewer.

Solution:

Let `b` and `d` be the width and depth of rectangular sewer and `D` be the diameter of circular sewer.

Here, width of rectangular sewer is, `b=2.5 d`

For hydraulically equivalent sewers, discharge in both are same,

`Q_R=Q_C`

or, `bd**1/n **((bd)/(b+2d))^(2/3)**(s)^(1/2)=(piD^2)/4**(d/4)^(2/3)**s^(1/2)`

Solving this equation for d, we get,

`d=0.531 D`

 Thus, the depth of rectangular sewer is 0.531 times the diameter of circular sewer.