# Consider a long sewer pipe, half full of water, slopingdownward at angle θ . Antoine Chézy in 1768 determinedthat the average velocity of such an open channel fl owshould be V ≈ C √R tan θ , where R is the pipe radius andC is a constant. How does this famous formula relate to thesteady fl ow energy equation applied to a length L of thechannel?

Question

Consider a long sewer pipe, half full of water, sloping
downward at angle θ . Antoine Chézy in 1768 determined
that the average velocity of such an open channel fl ow
should be V ≈ C √R tan θ , where R is the pipe radius and
C is a constant. How does this famous formula relate to the
steady fl ow energy equation applied to a length L of the
channel?