Heat generated due to friction in a pipe.
Heat generated due to friction in a pipe.
(OP)
Long time lurker, first time poster. I've searched here and Google in general without finding a reasonable solution.
I'm trying to find an equation that I could use in Excel that would tell me the temperature gain from friction flow in a pipe.
Thank you ahead of time for any information that you have and feel free to ask for any clarificaiton I might add.
I'm trying to find an equation that I could use in Excel that would tell me the temperature gain from friction flow in a pipe.
Thank you ahead of time for any information that you have and feel free to ask for any clarificaiton I might add.





RE: Heat generated due to friction in a pipe.
You must know that it is an unusual question since friction is relatively small and in real world terms it is usually neglected
RE: Heat generated due to friction in a pipe.
I’m looking at a system for the transportation of Propane and Butane through a 14"/16" pipe at 8600 BPH. This wouldn't be considered adiabatic as heat would be lost to the surrounding area.
I'm trying to approach this by breaking down the temperature gain/loss into three components. Heat loss from the Joules-Thompson effect, heat loss to the surrounding ground, and heat gained from friction. I have the first two parts, just not the last.
I understand that generally the heat generated from friction is ignored, but when trying to model match, I am finding that I require much lower heat transfer coefficients than seems reasonable in order to match my data. This makes me believe that another factor, such as heat from friction, is occurring.
I hope this helps.
RE: Heat generated due to friction in a pipe.
RE: Heat generated due to friction in a pipe.
Are you saying
" I have a gas flowing thru a pipe embedded in earth initial state T1,p, T=, distance along pipe, meters , flow rate."
If this is the system, then you have to write the dynamic flow equations using the standard mechanical and thermal equations that are involved.
The Joule- Thomson effect, I believe is not a heat loss term, but a temperature change due to the reduction of pressure caused by friction in the pipe.
So this complex problem involves fluid flow and thermal equilibrium.
I believe you should be working with internal energy and flow work.
It would help if you drew us a picture of the system.
RE: Heat generated due to friction in a pipe.
RE: Heat generated due to friction in a pipe.
RE: Heat generated due to friction in a pipe.
Katmar Software - AioFlo Pipe Hydraulics
http://katmarsoftware.com
"An undefined problem has an infinite number of solutions"
RE: Heat generated due to friction in a pipe.
RE: Heat generated due to friction in a pipe.
This is a Google Earth screen shot of the system. The blue line on the west side has a 14" diameter and the rest is 16". This is all buried pipe and is about 65 miles long.
When I say BPH, I mean barrels(oil) per hour or just over 100 gpm. The Propane/Butane enters the pipe at 100F and ~865psi. I know the density, specific heat, viscosity, JT coeff, overall heat transfer coeff, etc. For this specific case, I'm using 90F ground temp. I can already calculate my head/pressure loss, I just need to refine my temperature calculations.
In my spreadsheet, I have set it up to where the pipe is broken into ~170ft segments, and for each segment, I'm trying to calculate the deltaT from the JT effect, friction, and the temp loss to the surrounding ground independently of each other. I am summing each respective deltaT to get the end temperature at each segment. Am I wrong in my analysis method?
I understand that generally the DeltaT from friction is negligible, but in this case with the viscosity and velocity that it might have a greater role than most would think.
Does anybody have an equation describes what I'm looking for?
I hope this helps.
RE: Heat generated due to friction in a pipe.
This process does not include heat loss, as the enthalpy of the fluid does not change.
RE: Heat generated due to friction in a pipe.
p1v1 +u1 + V1^2/2g+q=P2v2 +u2 +V2^2/2g
p pressure
u= internal energy
v specific volume
V= velocity
q= heat added from ground= U*(Tg-T)*Area pipe segment.
At the entrance of each pipe segment, you have u1(T1) and if, as you say you know the pressure drop, p1-p2, then with some minor assumptions on V, you should easily get T2 as a function of the p2 and u2.(per Joule Thomson) You could use iteration, if your assumptions are inaccurate, but a solution for each segment is pretty fast if the segment lengths are small enough.
BTW, 8600BPH doesn't translate to 100gpm.
RE: Heat generated due to friction in a pipe.
Assuming that all the friction, as pressure loss, is converted to heat, with no change of phase, consider that:
• Δpf is the pressure drop due to friction, expressed in N/m2
• ρ is the fluid density, expressed in kg/m3
Then,
• Δpf/ρ has the dimensions of energy per unit mass:
Thus, knowing the specific heat of the fluid one can estimate the "resulting" temperature climb.
RE: Heat generated due to friction in a pipe.
At 100F the vapor pressure of propane is 187 psi and the start pressure is
865 psi. How does J-T happen in this environment?
RE: Heat generated due to friction in a pipe.
The J-T effect happens on real fluids (liquids and gases) but in this particular case there is an insignificant heat up effect on the order of -0.003oF/psi for butane and about -0.0004 oF/psi for propane. See thread124-132825: JOULE-THOMSON EFFECT.
RE: Heat generated due to friction in a pipe.
W'cdT/dx=-vdp/dx +U*Pi*D*(Tg-T)
W' flow rate lb/hr
D pipe OD
c specific heat of liquid
pi 3.14
Tg ground temperature
T temperature of liquid along pipe
The first term on the RHS is fairly constant c(due to constant pressure gradient from friction) over a constant diameter pipe
after division of eq(1) by w'c and simplifying substitutions
(2) d(T-Tg)/dx=K+B*(Tg-T)
where
K=-vdp/dx/w'c
B= U*Pi*D/w'c
The solution to (2) is
T-Tg=K/B+(Ti-Tg-K/B)exp(-Bx)
T=Tg+K/B+(Ti-Tg-K/B)exp(-Bx)
Ti= entering temperature of fluid
No need for spreadsheet.
RE: Heat generated due to friction in a pipe.
Thank you so much! You equations make sense and have helped me greatly!