need help understanding how Length and Diameter were calculated. please show all steps.

a. V-102 High-Pressure Phase Separator From Table 11.6, the following heuristics are used: Rule 3 Vertical vessel Rule 4L/D between 2.5 and 5 with optimum at 3.0 Rule 5 Liquid holdup time is 5min based on 1/2 volume of vessel Rule 9 Gas velocity u is given by u=k0l1m/s where k=0.0305 for vessels without mesh entrainers Rule 12 Good performance obtained at 30%100% of u from Rule 9 ; typical value is 75% From Table 1.5, Vapor flow = Stream 8=9200kg/h,P=23.9bar,T=38C Liquid flow = Streams 17+18=11,570kg/h,P=2.8 bar, T=38C v=8kg/m3 and l=850kg/m3 (estimated from Table 1.7) From Rule 9,u=0.0305[850/81]0.5=0.313m/s Use uact=(0.75)(0.313)=0.23m/s Now mass flowrate of vapor =uvD2/4=9200/3600=2.56kg/s Solving for D,D=1.33m From Rule 5, the volume of liquid =0.5LD2/4=0.726Lm3 5 min of liquid flow =(5)(60)(11,570)/850/3600=1.13m3 Equating the two results above, L=1.56m From Rule 4,L/D should be in the range 2.5 to 5 . For this case L/D=1.56/1.33=1.17 Because this is out of range, change to L=2.5D=3.3m. Heuristics from Table 11.6 suggest that V-102 should be a vertical vessel with D=1.33m,L=3.3m From Table 1.7, the actual V102 is a vertical vessel with D=1.1m,L=3.5m It should be concluded that the design of V-102 given in Chapter 1 is consistent with the heuristics given in Table 11.6. The small differences in L and D are to be expected in a comparison such as this one