The Hazen–Williams equation has the advantage that the coefficient C is not a function of the Reynolds number, but it has the disadvantage that it is only valid for water.
[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.
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: