PROBLEM $1$: A $2-$m long horizontal, galvanized iron, circular cross$-$section pipe with internal diameter of $1$ cm has water flowing through it steadily. The water discharges into the atmosphere and on the upstream end a circular pump provides the pressure to drive the flow. The temperature is $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ If the steady water flow rate is $\backslash (80\backslash$mathrm$\{$~cm$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ),$ estimate the gage pressure the pump needs to provide for this flow. What assumptions did you have to make to come up with your estimate?

PROBLEM $2$: In the same system above, the flow rate is now reduced to $\backslash (5\backslash$mathrm$\{$~cm$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$ What is the pressure the pump has to provide for this flow rate?