Hi all,

I'm inquiring as to the steps involved in determining head loss equation from following kinetic energy work done equality.

$\displaystyle \frac{d}{dt}$ ($\displaystyle \frac{1}{2}$ $\displaystyle LU^2)$ = -$\displaystyle \frac{1}{2}$ $\displaystyle \ n C D L U^3$

I'm looking for the methodology to determine the velocity U as a function of x, the distance traveled. the following chain rule relation is used

$\displaystyle \frac{du}{dx} $ = $\displaystyle \frac{1}{U}$ $\displaystyle \frac{dU}{dt}$

Integrating with respect to x yields the following equality

$\displaystyle \frac{U}{U_0}$ = exp(-$\displaystyle \frac{n C D x}{2})$

Can anyone help me with the steps involved in going from the first equation to the final equality