A pipeline system consists of two pipes in series. The first pipe is $3$ meters long, and the second pipe is $84$ meters long. The total pressure drop for crude oil flowing through the system at a volumetric flow rate of $60$ L$/$min is $20$ meters. The diameter of the first pipe, which is $3$ meters long, is $7\mathrm{.}5$ cm$.$ To achieve the given pressure drop at the specified flow rate, what should be the diameter of the second pipe, which is $84$ meters long? The viscosity of the oil is $0\mathrm{.}0261$ kg$/$m$.$s$,$ and its density is $900$ kg$/$m$.$