Turbulence Kinetic Energy in pipe flow

What is the equation to estimate the turbulence kinetic energy per unit volume in pipe flow? Any information is appreciated.

In most practical pipes for everyday use, the flow is primarily turbulent. The kinetic energy would just be 1/2 m*v^2, where m is the mass of a section of fluid in the pipe and v is the velocity of that fluid where you picked it.

You could solve backwards for the velocity if you knew the head loss and friction factor in the pipe (can get off a Moody chart using pipe surface roughness and the turbulence of the flow).



Science Advisor
Turbulent kinetic energy is particularly useful when looking at CFD turbulence models. For example, the very standard k-ε model uses turbulent kinetic energy as one of the "transported" variables representing the turbulent properties.
Thanks for your replies.

I agree that the MEAN kinetic engergy per unit mass can be approximated as,

0.5*(U^2) where U is the average velocity in pipe.

Is there a similar equation that can be used to estimate the Turbulence kinetic energy per unit mass in pipe flow? such as

0.5*f(U'^2) wehre f is the friction factor

Or some other equations?

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