Applied Hydraulics #$3\mathrm{.}5\mathrm{.}14.$

A cast$-$iron pipeline was installed $20$ years ago with a friction factor $($measured$)$ of $0\mathrm{.}0195$ and a roughness height $($e$)$ of $0\mathrm{.}26mm.$ The horizontal pipeline is $2,000m$ long and has a diameter of $30cm.$ Significant tuberculation has occurred since it was installed, and field tests are run to determine the existing friction factor. A pressure drop of $366,000$ Pascals is measured over the pipeline length for a flowrate $($at $20C)$ of $0\mathrm{.}136\frac{m^3}{s}.$ Determine the existing friction factor $($effective$)$ and the existing roughness height. Note: The friction factor is called "effective" since the loss of flow area due to tuberculation contributes to the reduced flow rate. Assume that minor losses are negligible.