# (Cp/k)^0.4

The Nusselt number inside of a tube supposedly is
Nu = 0.0255(Re)^0.8(Cp/k)^0.4
The units are lengh*time/mass or 3429 cm sec / gm for air at 350 K.
Elsewhere in the English unit based book 0.73 is given as the value
for Cp/k and is raised to the 0.3 power or 0.91.
How do you raise units to some fractional power?
The book has several typos but I can't get this one.
Bret Cahill
Dear Bret Cahill:
It is wrong. Pitch it now.
I suggest that it is describing a particular empirical relationship, that will not survive scaling.
David A. Smith
They somehow got Cp/k swapped with the Prantl number.
I was using it as a check. I always look at several different sources.
Bret Cahill
You shouldn't have to raise units to a fractional power.
The Nusselt number and the Reynolds number are both dimensionless numbers.
Where your equation has (Cp/k) it is wrong. This term should also include the viscosity. When you do that, it becomes the Prandtl number, which is also dimensionless.
This correlation is very well known. It is called the Dittus-Boelter equation or Dittus-Boelter correlation. Try googling it.
Olin Perry Norton
.
This has the Dittus-Boelter equation and much else.
Olin Perry Norton
.
This has the Dittus-Boelter equation and much else.
Olin Perry Norton
Wilhelm was a busy man. There are three dimensionless numbers named for him: Heat transfer, Mass transfer, and Film thickness.
You are interested in the first named number. This is an on line Nu calculator, couched in SI units
Another way of thinking about Nu is as the ratio of total heat transfer to conductive heat transfer. The units are meant to coancel, leaving only a number.
Your question, "how do you raise units to a fractional power?" probably doesn't mean what it says. But to answer the question as given: for any power of any number, multiplying their logarithms and taking the antilog provides the answer. The everyday route to raising a number by a fractional power is a calculator with an X^Y function.
Brian Whatcott Altus OK
It's a terrible embarrasment because I'm always promoting a better heat transfer culture.
Even worse, I looked at the units for a quantity that would make it dimensionaless and didn't see 1/viscosity.
I better lay off the juice for awhile.
Bret Cahill
Why do you always end up on a homeland security list whenever you download HX material?
The cold war is over. They need to go after the guys in the caves, not us.
Bret Cahill
Hmmmm...wild guess now...... if a data miner is looking for keywords on all newsgroups, and listening for keywords on all phone conversations and all telecomms channels, do you think it might just possibly be interested in an acronym for High Explosives?
:-)
Brian Whatcott Altus OK

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