(adsbygoogle = window.adsbygoogle || []).push({}); 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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# Thermodynamics Change in Gas Temperature along pipe

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