Solved problem on design selection for a process industry
Solved problem on design selection for a process industry
The chief engineer of refinery operations is not satisfied with the preliminary design for storage tanks to be used as part of a plant expansion programme. The engineer who submitted the design was called in and asked to reconsider the overall dimensions in the light of an article in the Chemical Engineer, entitled "How to size future process vessels?"
The original design submitted called for 4 tanks 5.2m in diameter and 7 m in height. From a graph of the article, the engineer found that the present ratio of height to diameter of 1.35 is 111 % of the minimum cost and that the minimum cost for a tank was when the ratio of height to diameter was 4 : 1. The cost for the tank design as originally submitted was estimated to be Rs. 9,00,000. What are the optimum tank dimensions if the volume remains the same as for the original design? What total savings may be expected through the redesign?
Given Data
Number of tanks = 4
Original design
Diameter of the tank = 5.2 m
Radius of the tank = 2.6 m
Height of the tank = 7 m
Ratio of height to diameter (h/d) = 1.35
Cost of the old design = 111% of the cost of the optimum design
Solution
(a) Original design
Volume/tank = π r2 h = π (2.6)2 7 = 148.72 m3
(b) New design
Optimal ratio of the height to diameter = 4: 1
h:d = 4:l
h/d = 4 / 1
d = h/4
r = d/2 = (h/4) / 2 = h/8
Since, the volume remains the same
Therefore,
Volume = π r*2 h = 148.72 m3
π (h/8)*2 h = 148.72 m3
h*3 = 3028.48
h = 14.47 m
r = h / 8 = 14.47 / 8 = 1.81 m
Therefore,
Diameter of the new design = 1.81 x 2 = 3.62 m
Cost of the optimum design = 900,000 x (100/111) = Rs. 8,10,810.81
Expected savings by the redesign (optimum design) = Rs. 9,00,000 - Rs. 8,10,810.81
= Rs. 89,189.19
