$10\mathrm{.}10$ A toluene surge drum has capacity $500$ gal and is normally operated $60\%$ full at $100$F under $300$ psig of hydrogen in the head space using a level controlled outflow. The normal flow rate into the vessel is $30,000$ lb$/$hr$.$ Determine the vessel dimensions if the vessel is vertically mounted. Evaluate the relief loads for the blocked outflow and external fire cases and hence determine the relief valve size.