Cooling water flows through a jacketed reactor and is controlled by a valve. The cooling water flow rate through the jacket obeys the following relation:

where the pressure is in psi and the flow rate q is in gal/min. The pressure drop across the cooling jacket and other associated plumbing is described with the following equation:

The steady-state cooling water flow rate is designed to be 90 gal/min when the valve is half open. It is suggested that an equal percentage valve be used to make a linear relationship between flow q and lift l when installed in the flow loop.

(a) What value of R between 20 and 50 will create the most linear relationship?