text: Once this relationship was established by Chézy, many engineers and physicists (see the below section Authors of flow formulas) continued to search for ways to improve Chézys equation. A slight oversight of Chézys formula was determined by the research of these colleagues. They determined that the velocitys slope dependence in Chézys formula (V:S) was reasonable, but that the velocitys dependence on the hydraulic radius (V:R) was not reasonable and that the relationship was closer to (V:R). Many formulas based on Chézys formula have been developed since its discovery by these contemporaries and others, and differing formulas are more suitable in differing conditions.
  The Chézy formula provided a substantial foundation for a new flow formula proposed in 1889 by Irish engineer Robert Manning. Mannings formula is a modified Chézy formula that combines many of his aforementioned contemporaries work. Mannings modifications to the Chézy formula allowed the entire similarity parameter to be calculated by channel characteristics rather than by experimental measurements. The Manning equation improved Chézys equation by better representing the relationship between R and velocity, while also replacing the empirical Chézy coefficient () with the Manning resistance coefficient (), which is also referenced in places as the Manning roughness coefficient. Unlike the Chézy coefficient () which could only be determined by field measurements, the Manning coefficient () was determined to remain constant based on the material of the wetted perimeter, allowing for a standardized table of values to be developed that could reasonably estimate flow velocity. While field measurements remain the most precise way to obtain either Chézy or Manning coefficients, the standardized values that were developed with the use of the Manning formula provided a much-desired simplicity to open-channel flow estimates.