Solve the following three problems using:

$1.$ Darcy$-$Weisbach equation

$2.$ Hazen$-$Williams equation

$3.$ Manning equation

For the Darcy$-$Weisbach equation, calculate the friction factor using:

$1.$ Moody Chart

$2.$ Swamee$-$Jain Equation

Show all your calculations and present the final results in the table below:

Find the head loss due to friction in galvanized iron pipe of $30$ cm diameter and $50$ m long through which water is flowing at a velocity of $\backslash (3\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Assume that the water is flowing at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

Problem $2$:

Compute the discharge capacity of a $3$ m diameter wood stave pipe in its good condition carrying water at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The head loss of the pipe is found to be $2$ m per one km$.$

Problem $3$:

A pipeline is designed to carry crude oil $(\backslash (\backslash$mathrm$\{$S$\}.\backslash$mathrm$\{$G$\}=0\mathrm{.}93,$ v$=10^\{-5\}\backslash$mathrm$\{$~m$\}^\{2\}/\backslash$mathrm$\{$s$\}\backslash ))$ with a discharge of $\backslash (0\mathrm{.}10\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash )$ and a head loss per kilometer of $50$ m $.$ What diameter of steel pipe is needed? Available pipe diameters are $20,22,$ and $24$ cm $.$ Roughness of the commercial steel pipe is $\backslash (46\backslash$mu $\backslash$mathrm$\{$~m$\}\backslash ).$