Trial$-$and$-$Error Solution for Heated Hydraulic Drainage. In a hydraulic project a cast iron pipe having an inside diameter of $0\mathrm{.}15m$ and a $300-m$ length is used to drain wastewater which is also being heated from $10C$ to $30C.$ Use an average temperature of $20C$ for bulk physical properties. Assume that the pipe wall temperature is an average of $10C$ higher than the average bulk temperature so that a correction can be made for the effect of heat transfer on the friction factor. The available head is $4\mathrm{.}6m$ of water. Neglecting any losses in fittings and joints in the pipe, calculate the flow rate in $m\frac{3}{s}.($Hint: Assume the physical properties of pure water. The solution is trial and error since the velocity appears in $N_{Re},$ which is needed to determine the friction factor. As a first trial, assume that $v=1\mathrm{.}7\frac{m}{s}.)$