[4] Henri Pitot discovered that the velocity of a fluid was proportional to the square root of its head in the early 18th century.
It takes energy to push a fluid through a pipe, and Antoine de Chézy discovered that the hydraulic head loss was proportional to the velocity squared.
where: The equation is similar to the Chézy formula but the exponents have been adjusted to better fit data from typical engineering situations.
A result of adjusting the exponents is that the value of C appears more like a constant over a wide range of the other parameters.
Taking the general form and exponentiating each side by 1/0.54 gives (rounding exponents to 3–4 decimals) Rearranging gives The flow rate Q = V A, so The hydraulic radius R (which is different from the geometric radius r) for a full pipe of geometric diameter d is d/4; the pipe's cross sectional area A is π d2 / 4, so When used to calculate the pressure drop using the US customary units system, the equation is:[12] where: When used to calculate the head loss with the International System of Units, the equation will then become where: