temperature rise of fluid due to pipe friction

[mechanicaldup]

What fomula could be used to detemine the temperature rise of a liquid due to the pipe friction?

have a nice day

 

[MortenA]

Do an energy ballance!

The energy lost to friction must be turned into heat - this heat is on the other side exchange with the surroundsings.

Best regards

Morten

 

[aspearin1]

I cannot recall the equation off hand, but I do remember getting one from Perry's Chemical Engineering Handbook; 6th edition a couple years ago.

ChemE, M.E. EIT
"The only constant in life is change." -Bruce Lee

 

[JStephen]

Assuming you know pressure in and pressure out; it then becomes a simple thermodynamics problem. Take the pipe as the free-body diagram. You could assume adiabatic conditions and solve for outlet temperature or assume constant temperature and solve for heat out.

 

[sailoday28]

h= spec. enthalpy
v= spec. volume
p=pressure
u=velocity
F=friction, (f/d)u^2/2
s spec. entropy
T=abs. temp
Q=heat transfer
x=distance
T(ds/dx)= uF+Q
dh/dx-vdpdx=uF+Q
Cp=spec heat at const press.
for Adiabatic conditions and v approx constant
Cp(Delta T)-v(Delta p)=uF(pipe length)

Knowing pressure drop, spec. heat,spec. vol, velocity and friction factor, --Solve for Temp difference.

 

[sailoday28]

If the mu, the J-T coef is available my last post could be modified for andiabatic and highly incompressible flow as follows:

energy equations dh+du^2/2=0
highly incomp flow yields approximation of dh=0 perfect for use of J-T

dh/dx-vdpdx=uF+Q
dh/dx-vdpdx=uF adiabatic
-vdpdx=uF for dh=0

-v(dp/dT)dT/dx=uF
-v/mu(dT/dx)=uF
delta temp= -(mu)(uF/v)*length of pipe

Comments please!

 

[lilliput1]

Pump bhp = GPM x Ft Head /(3960 x Pump Eff)

With motor out, driven equipment in, heat gain Btu/hr Q = bhp x 2545 = gpm x 500 x (°F Td)