Determine diameter and velocity of a circular sewer at a slope of 1 in 500 when it is running just full at a discharge of 1m3/sec. The value of n in Manning's formula is 0.012. What will be discharge and velocity when flowing half full for same slope?

Solution:

When running full,

`Q=1=(pi d^2)/4**(1/0.012)**(d/4)^(3/2)**(1/500)^(1/2)`

Solving this, we get,

`d=0.95\ m`

 and the velocity is, `v=Q/A`

 `=1/((pi**0.95^2)/4)`

 `=1.411\ m^3/s`

 Again, when the sewer is running half full,

 `Q=(pi d^2)/8**(1/0.012)**(d/4)^(3/2)**(1/500)^(1/2)`

or, `Q=0.5\ m^3/s`

and the velocity is,

`v=0.5/(pi*0.95^2/8)`

`=1.41\ m/s`

Solution:

When running full,

`Q=1=(pi d^2)/4**(1/0.012)**(d/4)^(3/2)**(1/500)^(1/2)`

Solving this, we get,

`d=0.95\ m`

 and the velocity is, `v=Q/A`

 `=1/((pi**0.95^2)/4)`

 `=1.411\ m^3/s`

 Again, when the sewer is running half full,

 `Q=(pi d^2)/8**(1/0.012)**(d/4)^(3/2)**(1/500)^(1/2)`

or, `Q=0.5\ m^3/s`

and the velocity is,

`v=0.5/(pi*0.95^2/8)`

`=1.41\ m/s`