Two pressure vessels in a plant are connected by a series of pipes and filters. The pressures in each vessel are different in this dynamic situation.
The pressures, relative to a constant reference level, in vessel 1 and vessel 2 are given by
respectively at time
 . They are governed by the following pair of first order, coupled differential equations:
where a = -18, b = 7, c = -14, d = 3
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(i) |
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Find the pressures in each pressure vessel if the initial pressures in vessel 1 and vessel 2 are
and
.
For this part of the question give the pressure in pressure vessel 1 as a function of t.
Omit the "
= " (8 marks)
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| Your Answer: |
(-5e^(-4t))+15e^(-11t) |
| Comment: | The particular solution is
= " "
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(ii) |
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What is
as a function of t?
Omit the "
= "
(8 marks)
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| Your Answer: |
(-10e^(-4t))+15e^(-11t) |
| Comment: | The particular solution is
= " "
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(iii) |
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What is the pressure in pressure vessel 1 at t = 0.06?
Give your answer to AT LEAST TWO PLACES OF DECIMALS. Put in this value only
ie. omit the "
= " (2 marks) |
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| Your Answer: |
3.819630712 |
| Comment: |
= 3.819630712
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(iv) |
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What is the pressure in tank 2 at t = 0.06?
Give your answer to AT LEAST TWO PLACES OF DECIMALS. Put in this value only
ie. omit the "
= " (2 marks) |
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| Your Answer: |
-.113508593 |
| Comment: |
= -.113508593
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