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Thermodynamics Change in Gas Temperature along pipe 
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#1
Jul108, 03:31 AM

P: 5

1. The problem statement, all variables and given/known data
Nitrogen beginning at 50^{o}C 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 20^{o}C. 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'  C_{p}  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  Q_{dot} /l = 2Pi.k.(T_{2}T_{1})/In(r_{2}/r_{1}) Q_{dot} = Heat Loss l = Length k = Thermal Conductivity T = Temperatures r = Radius W_{dot}  Q_{dot} = m_{dot}.C_{p}.(T_{2}T_{1}) W_{dot} = Work Energy In Q_{dot} = Heat Loss m_{dot} = mass flow rate C_{p} = Specific Heat T = Temperatures 3. The attempt at a solution using k = 15 (Which is the k of Stainless Steel) I used Q_{dot} /l = 2Pi.k.(T_{2}T_{1})/In(r_{2}/r_{1}) which gave me a figure of 8.653 x 10^{3} for Q_{dot} Then to calculate m_{dot} i used the following  m_{dot }= V_{dot} / v where V_{dot} = Volume flow rate and v = specific volume V_{dot} = 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} m^{3}/s v = R.T_{1} / P where R = Gas Constant which is 0.294 kJ/(kg.K) T_{1} is temperate 1 which is 323K and P is pressure which is 1 bar (1 x 10^{5}Pa) this gives v to be 9.4962 x 10^{4} m^{3}/kg using these m_{dot} becomes 26.32632 x 10^{3} kg/s Now using W_{dot}  Q_{dot} = m_{dot}.C_{p}.(T_{2}T_{1}) I rearrage to get T_{2} on its own therefore T_{2} = (Q_{dot} / m_{dot}.C_{p}) + T_{1} note that W_{dot} = 0 and so has been removed Therefore i get an answer of 50.3^{o}C 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. 


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