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Design-of-sewers-Tutorial

Calculate velocity of flow and discharge in a circular sewer having diameter `1` m and laid at a gradient of `1:600` and
  • running full and
  • running half full.
Take N = 0.012.

Solution:

From Mannings formula, we have, the velocity of flow is,

`v=1/n R^(2/3)S^(1/2)`

Where `R=A/P` is the hydraulic radius and `S` is the gradient

Case I: When the sewer is Running Full:

`A=(Pid^2)/4=(pi**1^2)/4=0.785\ m^2`

and `R=A/P=((Pid^2)/4)/(pi d)`

`=d/4=0.25\ m`

Thus, `v=1/0.012**0.25^(2/3)**(1/600)^(1/2)`

`=1.35\ m/s`

And the discharge is,

`Q=Av=0.785**1.35=1.059\ m^3/s`

Again for the sewers running half full,

`A=1/2(Pid^2)/4=1/2(pi**1^2)/4=0.392\ m^2`

and `R=A/P=((Pid^2)/8)/((pi d)/2)`

`=d/4=0.25\ m`

Thus, `v=1/0.012**0.25^(2/3)**(1/600)^(1/2)`

`=1.35\ m/s`

And the discharge is,

`Q=Av=0.392**1.35=0.529\ m^3/s`

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Take N = 0.012.

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Sanitary-Engineering