§ 11.2.2.2. Pressure and Weir Flow

Pressure flow occurs when the upstream water surface comes in contact with the low cord of the bridge and a backwater conditions occur. If the downstream side of the bridge low cord is not in contact with the bridge, then a sluice gate type of equation is used (FHWA, 1978). See Figure and Equation 11.2.2.2A on the following page.

(Equation 11.2.2.2A)

Q = Total discharge through the bridge opening (ft. /s)
C = Coefficients of discharge for pressure flow
A _b = Net area of the bridge opening at section BU (ft. )
y ₃ = Hydraulic depth at section 3
D _b = Vertical distance from maximum bridge low chord to the mean river bed elevation at section BU (ft.)
g = Gravitational acceleration (32.2 ft./s )
⍺ ₃ = kinetic energy correction coefficient (FHWA HDS-1 1978)
v ₃ = Velocity upstream at section 3

Figure 11.2.2.2.A - Sluice Gate Type Pressure Flow
(Source TxDOT Hydraulic Design Manual)

The orifice equation will be used if both up and downstream of the bridge are submerged. See Figure 11.2.2.2B on the following page.

(Equation 11.2.2.2B)

Q=CA(2gH) ^0.5

C = Coefficient of discharge for fully submerged pressure flow. Typical value of C is 0.8
H = The difference between the energy gradient elevation upstream and the water surface elevation downstream (ft.)
A = Net area of the bridge opening (ft )

Figure 11.2.2.2.B - Orifice Type Pressure Flow
(Source TxDOT Hydraulic Design Manual)

Should flow be over the bridge and the roadway approaching the bridge, then the standard weir equation is used to calculate flow. See Figure 11.2.2.2.C.

(Equation 11.2.2.2C)

Q=CLH ^3/2

Q = Total flow over the weir (ft. /s)
C = Coefficients of discharge for weir flow
L = Effective length of the weir (ft.)
H = Difference between energy upstream and road crest (ft.)

Figure 11.2.2.2.C - Pressure and Weir Flow
(Source USACE HEC-RAS Reference Manual)

For more information regarding hydraulic computations, refer to USACE HEC-RAS Reference Manual.