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Calculate volume from first order transfer function

  1. Nov 13, 2015 #1
    1. The problem statement, all variables and given/known data

    In a gas pipeline a mixture of hydrogen in air is transported. Usually, the hydrogen content of
    the gas is 1 volume %. It is well below the lower explosive limit as a hydrogen / air
    mixture is 4 % by volume hydrogen. gas pipeline is positioned a detector that activates an alarm if the
    detects a hydrogen content in the gas of 3% by volume or more. The detector's dynamic behavior may be described as a first order system with reinforcement 1 and the time constant of 5 seconds.
    The flow rate of the gas is constant 1 m3 / second.

    Because of incorrect operation increases the gas hydrogen content suddenly from the before mentioned 1% to 7%.

    A) How many m3 explosive gas (gas with a hydrogen content ≥ 4%) passes the detector before the alarm goes off?


    2. Relevant equations
    X'(s)/Xi'(s)=1/(5s+1)

    3. The attempt at a solution

    Xi'(s)=7-1/s=6/s
    then X'(s)=[1/(5s+1)]*6/s --> X'(s)=6/[s(5s+1)] -->
    Inverse Laplace --> X'(t)=6(1-e^(-t/5))
    X'(t)=X(t)-[Xi(t)ss] --> Pm(t)=6[1-e^(-t/5)]+1
    This gives
    4=6*[1-e^(-t/5)]+1 --> t=5.5 s --> V=1 m/s*5.5s = 5.5 m3

    I think something is wrong with the calculations, can I use the volume fraction directly like the above or have I missed something ?

    Any help will be very appreciated, thankyou
     
  2. jcsd
  3. Nov 18, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Nov 19, 2015 #3

    rude man

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    Make an electric analog: you have an R-C low-pass filter, Y(s) = X(s)/(Ts + 1). What is the initial condition y(0+)? What is the input X(s)? How much time passes before the output reaches the detector trip point?
     
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