# Thermodynamics Change in Gas Temperature along pipe

1. Jul 1, 2008

### daz18983

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.

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