5. An engineer is designing a pressure vessel, and selects an initial concept design consisting of a cylinder or length L, and radius r, both measured in metres, as shown in figure Q6. The volume of the vessel should be 1200 litres. The wall of the vessel will be a constant thickness throughout. The engineer wants to minimise the amount of material used in order to minimise the cost. Q6. Cont. Q6. Cont./ MEE1001/2021 Figure Q6 (a) Determine expressions for the surface area and the volume of the tank in terms of r and L. Hence find an expression for surface area in terms of r only. [4 marks] (b) Determine the combination of radius and length that will require the minimum amount of material to be used. You should use an appropriate method to verify that it is a minimum.

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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23:38 Fri 22 Jul
Q6.
4 of 6
Q6. Cont.
library.qol.qub.ac.uk - Private
Q7.
An engineer is designing a pressure vessel, and selects an initial concept design consisting of a
cylinder or length L, and radius r, both measured in metres, as shown in figure Q6. The volume
of the vessel should be 1200 litres. The wall of the vessel will be a constant thickness throughout.
The engineer wants to minimise the amount of material used in order to minimise the cost.
4% 1
[1 marks]
Figure Q6
(a) Determine expressions for the surface area and the volume of the tank in
L. Hence find an expression for surface area in terms of r only.
Q6. Cont./
MEE1001/2021
rms of r and
[4 marks]
(b) Determine the combination of radius and length that will require the minimum amount of
material to be used. You should use an appropriate method to verify that it is a minimum.
[10 marks]
Transcribed Image Text:23:38 Fri 22 Jul Q6. 4 of 6 Q6. Cont. library.qol.qub.ac.uk - Private Q7. An engineer is designing a pressure vessel, and selects an initial concept design consisting of a cylinder or length L, and radius r, both measured in metres, as shown in figure Q6. The volume of the vessel should be 1200 litres. The wall of the vessel will be a constant thickness throughout. The engineer wants to minimise the amount of material used in order to minimise the cost. 4% 1 [1 marks] Figure Q6 (a) Determine expressions for the surface area and the volume of the tank in L. Hence find an expression for surface area in terms of r only. Q6. Cont./ MEE1001/2021 rms of r and [4 marks] (b) Determine the combination of radius and length that will require the minimum amount of material to be used. You should use an appropriate method to verify that it is a minimum. [10 marks]
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