Use 10 steps of the golden-section search method to find the optimal dimensions for the cylindrical reactor vessel in Example 16.12. In that example, the dimensions of the vessel are given as the inside diameter, \(D=6.5 \mathrm{ft}\) and tangent-to-tangent length, \(\mathrm{L}=40 \mathrm{ft}\). These dimensions are not critical as long as the volume is maintained. Determine the optimal diameter and length if the permissible range of the aspect ratio, \(L / D\), is 1 to 50 .

Data From Example 16.12:-

An adiabatic reactor consists of a cylindrical vessel with elliptical heads, with an inside diameter of 6.5 ft (78 in.) and a tangent-to-tangent length of 40 ft (480 in.). Gas enters the reactor at a pressure of 484 psia and 800^∘F. Exit conditions are 482 psia and 850^∘F. The vessel will be oriented in a horizontal position. Estimate the vessel thickness in inches, weight in pounds, and purchase cost in dollars for a CE cost index of 600. The vessel contains no internals and the gas is noncorrosive. The barometric pressure at the plant site is 14 psia.

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S1 Styrene 25,000 lb/hr 300F 50 psia S4 E1 S3 Heatx -AP = 5 psi both sides U-50 -AP-5 psi E2 Heater U=75 Steam: 366F $10.00/million Btu $6 350F S5 100F E3 Heater U = 75 CW: 80F in 100F out $2.00/million Btu. -AP = 5 psi S2 Toluene 25,000 lb/hr 100F 90 psia Figure 21.15 Heat exchange network.