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21 October, 11:57

A process temperature is known to fluctuate with a frequency of 0.1 Hz. The engineer needs to monitor this process using a first-order thermocouple and wishes to have no more than 2% amplitude reduction.

a. What time constant of the thermocouple is needed?

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  1. 21 October, 15:48
    0
    t ≤ 0.31s

    Explanation:

    Given

    Frequency = 0.1Hz

    Dynamic Error:

    σ = 1 - M (σ)

    From the question

    σ = 1 - M (σ) ≤ 2%

    1 - M (σ) ≤ 0.02

    The above corresponds to

    M (σ) = 1 / (1 + (wt)) ² ≥ 100% - 0.02

    M (σ) = 1 / (1 + (wt)) ² ≥ 1 - 0.02

    M (σ) = 1 / (1 + (wt)) ² ≥ 0.98

    Since frequency = 0.1Hz

    w = 2πf =

    w = 0.628571428571428

    w = 0.628rads

    So, M (0.628) = 1 / (1 + (0.628t) ²) ≥ 0.98

    Solving 1 / (1 + (0.628t) ²) ≥ 0.98 we get that

    t ≤ 0.31s
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