Problem $8$: A pump with a capacity of $500$ liter$/$second can pump the flow against a pressure loss of $50$ kPa $.$ The distance between the well and the consumption center is $650$ m $.$ Choose a suitable material for the pipeline and find out the diameter of the most suitable pipe and the using an iterative approach. Water density $=1000k\frac{g}{m^3}$ and viscosity ${10}^{-3}$ Pa$.$s$.$

$($Hint: Take initial guess for Reynolds number as $25000$ in a smooth pipe. Two iterations are sufficient to find the final answer.$)$