Culverts in inlet control are designed on the basis of one of three criteria:
- Unsubmerged inlet
- Submerged inlet
- Transition zone
If the inlet is unsubmerged, the culvert is basically a weir (criteria #1) and the calculations are performed as such. If the inlet is submerged, the culvert is basically an orifice (criteria #2), and again, the calculations performed are virtually identical to that for an orifice. The transition zone between the two is a relatively undefined spot. Unfortunately, this is the most important part for designing a culvert, because you are trying to figure out the smallest culvert that flows full (basically).
We are quite familiar with the performance of weirs and orifices. The problem is that when you plot the headwaters produced by them on the same graph, they rarely intersect. A culvert, in its ideal design state at full flow, is transitioning from one to the other, so if they don’t intersect you can see the difficulty of determining a culvert headwater when it’s flowing full.
The Federal Highway Administration’s (FHWA) HDS-5 procedure involves calculating a dimensionless factor called: . Q is the design flow, A is the full flow area, and D is the diameter. If this factor is greater than 4.0 (2.21 in metric), the inlet is assumed submerged. If it is less than 3.5 (1.93 in metric) the inlet is unsubmerged. Anything in between is the transition zone.
The submerged inlet headwater (orifice) calculation is as follows:
HW = Headwater, m or ft
D = Diameter, m or ft
c = constant (looked up on tables)
Ku = unit conversion factor, 1.0 for US, 1.811 for metric
Q = Design Flow, ft3/s or m3/s
A = Full flow area, ft2 or m2;
D = Culvert diameter, ft or m
Y = constant (looked up on tables)
Ks = Slope correction factor, mostly -0.5 except for 0.7 mitered inlets
S = Culvert slope
The unsubmerged headwater (weir) calculation is as follows:
Hc = Specific head at critical depth, ft or m
K = constant (looked up on tables)
Now for the dreaded transition zone. HDS-5 allows you to perform a basic linear interpolation between unsubmerged (weir) flow at Q/AD0.5 =3.5 (metric: 1.93) and submerged (orifice) flow at Q/AD0.5 =4.0 (metric: 2.21). Simply calculate each one at those locations and interpolate linearly.
Software programs such as CulvertPro and HY-8 use a 5th degree polynomial curve to provide a smoother transition between weir and orifice flow. Although some engineers like to calculate things by hand, they are tedious, time consuming, and prone to error. It is strongly advisable to use software.
Don’t forget that inlet control is only one of two flow conditions required to determine the headwater. As a matter of fact, outlet control governs more often than inlet control.