Discussion
Consider the following statements about the time constant of a stirred tank.
1. It equals the volume divided by the volumetric flow rate.
2. After one time constant about 63 per cent of a step change has occurred.
3. A larger tank at the same flow responds more quickly.
Answer: A
Correct answer: 1 and 2 only
Statements 1 and 2 are correct: \( \tau = V/\dot{V} \), and the exponential response reaches \( 1-e^{-1} = 63 \) per cent of a step change in one time constant. Statement 3 is inverted - a larger tank at the same flow has a longer time constant and responds more *slowly*, which is precisely why a surge vessel is fitted to damp fluctuations.
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