Thermodynamics Change in Gas Temperature along pipe

  1. 1. The problem statement, all variables and given/known data

    Nitrogen beginning at 50oC is pumped along a 30m length of Stainless Steel pipe at a flow rate of 1.5 litres per minute. The Pipeline is at ambient temperature 20oC. Find the temperature of the Nitrogen upon it leaving the end of the pipeline.

    Pipe OD - 0.00635m
    Pipe ID - 0.00457m
    Pressure - 1bar

    The following data is taken from a copy of 'An Engineering Data Book' -

    Cp - Nitrogen at 20oC and 1 bar is 1.04 kJ/(kgK)

    2. Relevant equations

    From 'An Engineering Data Book' and 'Thermodynamics an Engineering Approach 4th Edition' i believed that i could work at the figures from the following equations -

    Qdot /l = 2Pi.k.(T2-T1)/In(r2/r1)

    Qdot = Heat Loss l = Length k = Thermal Conductivity T = Temperatures r = Radius

    Wdot - Qdot = mdot.Cp.(T2-T1)

    Wdot = Work Energy In Qdot = Heat Loss mdot = mass flow rate Cp = Specific Heat T = Temperatures

    3. The attempt at a solution

    using k = 15 (Which is the k of Stainless Steel)

    I used Qdot /l = 2Pi.k.(T2-T1)/In(r2/r1)

    which gave me a figure of 8.653 x 103 for Qdot

    Then to calculate mdot i used the following -

    mdot = Vdot / v

    where Vdot = Volume flow rate and v = specific volume

    Vdot = V / delta t

    where V = Volume which is 1.5 litres and delta t = 60 seconds (take from flow rate)

    therefore Vdot = 0.025 l/s = 25 x 10-5 m3/s

    v = R.T1 / P

    where R = Gas Constant which is 0.294 kJ/(kg.K) T1 is temperate 1 which is 323K and P is pressure which is 1 bar (1 x 105Pa)

    this gives v to be 9.4962 x 10-4 m3/kg

    using these mdot becomes 26.32632 x 10-3 kg/s

    Now using Wdot - Qdot = mdot.Cp.(T2-T1)
    I rearrage to get T2 on its own

    therefore T2 = (-Qdot / mdot.Cp) + T1
    note that Wdot = 0 and so has been removed

    Therefore i get an answer of 50.3oC which is obviously WAY wrong??? Can someone please help me with this. Even just a point in the right direction of the correct equations. This is not a homework or coursework question this an engineering question at work and i'm not too sure where to go with it.
     
  2. jcsd
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