Tube details:

Let us select 1 ¼ inch nominal diameter, 80 schedule, brass tubes of 12 ft in length

Outer tube diameter (d_o) = 42.16 mm

Inner tube diameter (d_i) = 32.46 mm

Tube length ( L ) = 12 ft = 3.6576 m

Surface area of each tube ( a ) = π × d_o× L =π × 42.164×10^-3 × 3.6576 = 0.4845 m²

Number of tubes required providing 10% overdesign (N_t) = A / a = (115/0.4845) ≈238

Tube pitch (triangular), P_T = 1.25 × d_o = 1.25 × 42.164 = 52.71 ≈53mm

Total area occupied by tubes = N_t × (1/2) × P_T × P_T × sinθ (where θ = 60°)

                                             = 238 × 0.5 ×(53×10^-3 )² × 0.866

                                             = 0.2894 m²

This area is generally divided by a factor which varies from 0.8 to 1 to find out the actual area. This allows for position adjustment of peripheral tubes as those can't be too close to tube sheet edge.

Actual area required = 0.2894/ 0.9 (0.9 is selected)

                                = 0.3216 m²

The central downcomer area is generally taken as 40 to 70% of the total cross sectional area of tubes. Consider 50% of the total tube cross sectional area.

Therefore, downcomer area = 0.5 × [ N_t × (π/4) × d_o ² ]

                                            = 0.5 × [238 × (π/4) × (0.04216)² ]

                                             = 0.1661 m²

Downcomer diameter = √[(4 ×0.1661)/π]

                                 = 0.460 m

Total area of tube sheet in evaporator = downcomer area + area occupied by tubes

                                                           = 0.1661+ 0.3216 m²

                                                           = 0.4877 m²

Tube sheet diameter = √[(4 ×0.4877)/ π]

                                = 0.788 m