# Mean temperature of a fluid in a pipe

Consider a pipe in which a fluid flows such that the pipe is at a higher temperature than the fluid. At any cross section of the pipe we get a varying temperature profile. We can define a mean temperature at this cross section, which is basically the value that would give us the same energy flow rate through the cross section as the varying temperature profile would. Using this we can come up with a relation for the mean temperature $$T_m$$

In this derivation, the enthalpy h of the fluid is substituted by $$c_p T$$, which means this temperature $$T$$ is in Kelvins. I say this because we can write enthalpy $$h= c_p T$$ only when we have given the value of enthalpy at $$T=0K$$ as $$0$$.

My question is -

Since the temperature T is in K, does that mean I have to always remember that whenever I substitute the temperature profile (temperature variation relation) in the formula for $$T_m$$ to determine $$T_m$$ I would have to do so in kelvins?

For instance in this practice problem they have given the temperature profile in Kelvins

• Ohh. What if the temperature profile in the question was given in Celsius. Could I substitute it in the formula for $T_m$ to get $T_m$ in degree Celsius? Or would I have to convert that profile first in kelvins and then substitute? Apr 19, 2022 at 15:02