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