$($Single pipe with pump$)$ The pump shown in the figure below adds a $16-$ ft head to the water being pumped from the upper tank to the lower tank when the flowrate is $1\mathrm{.}5f\frac{t^3}{s}.$ Determine the friction factor for the pipe $($a$)$ for the flow from the upper tank to the lower tank, $($b$)$ for the flow from the lower tank to the upper tank.

$($a$)f=$