Example

$h_f=\frac{10\mathrm{.}6}{C^{1\mathrm{.}85}}\frac{L}{D^{4\mathrm{.}87}}{Q}^{1\mathrm{.}85}$

Cost relation for a specific municipal water supply project:

$C=1563D^3-5928\mathrm{.}4D^2+7696\mathrm{.}9D-1611\mathrm{.}4$ for $0\mathrm{.}5mD2\mathrm{.}0m$

Where,

C: cost of the pipe $(\frac{\text{\$}}{m})$

D: pipe diameter $(m)$

Using William$-$Hazen Eqn with $C_w=100,$

plot the variation of the pipe cost with respect to capacity $(Q)$ for the slope of $0\mathrm{.}001.$

The minimum required discharge is $0\mathrm{.}5\frac{m^3}{s}.$

The increase in cost with respect to capacity should be less than $300(\frac{\text{\$}}{m})(\frac{m^3}{s}).$

Propose the optimum pipe size.