HY8:Polynomial Generation

Inlet control means that flow within the culvert barrel is supercritical and not capable of transmitting losses upstream. The determination of the headwater depth, therefore, is not found using the energy equation, but is the result of many scaled model tests. In HDS-5 (Appendix A), submerged and unsubmerged equations developed by the National Bureau of Standards from the scaled model tests were originally used to determine headwater depths. These equations required four coefficients, K, M, c, and Y. Unfortunately, once plotted, the transition zone between unsubmerged and submerged flow was not well defined. For the purposes of the HY-8 program, a fifth degree polynomial curve was fitted through the three regions of flow: unsubmerged, transition, and submerged (see equation below). Fifth degree polynomial coefficients were obtained for all combinations of culvert shape and inlet configurations.

${\frac {HW}{D}}=a+b\left[{\frac {Q}{BD^{1.5}}}\right]+c\left[{\frac {Q}{BD^{1.5}}}\right]^{2}+d\left[{\frac {Q}{BD^{1.5}}}\right]^{3}+e\left[{\frac {Q}{BD^{1.5}}}\right]^{4}+f\left[{\frac {Q}{BD^{1.5}}}\right]^{5}$