Problem $1$: CONSIDER THE FOLLOWING BASE CASE:There is a flow of $100$ liters per minute of water at a pressure of $5$ bar and $25\backslash$deg C that passes through a commercial steel pipe of $2$ in$.$ nominal diameter schedule $40($internal diameter $2\mathrm{.}067$ in$).$ Consider a $30$ m long pipe. Answer correctly and justifying with a clear procedure the following, with respect to the base case:

a$)$ How much will friction losses increase$/$decrease if $1$ in $(1\mathrm{.}049$ in ID$)$ nominal diameter pipe is used instead of $2$ in$?$

b$)$ How much will friction losses increase$/$decrease if the water flow increases from $100$ liters per minute to $150$ liters per minute?

c$)$ How much will the friction losses increase$/$decrease if the length changes from $30$ m to $50$ m$?$