Hydraulic Loss Coefficients for Culverts (2012)

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81 a = empirical coefficient to power law relationship A = sectional flow area of culvert barrel or channel [L2] A1 = control volume cross-sectional flow area at location 1 (see Figure 4-1) [L2] A2 = control volume cross-sectional flow area at location 2 (see Figure 4-1) [L2] Ach = channel cross-sectional flow area downstream of culvert outlet [L2] Aflow = average culvert flow cross-sectional area (equals A for full-pipe flow) [L2] Ai = component flow area resulting from the partitioning of a composite-channel into subareas between the boundary roughness materials [L2] Ap = culvert cross-sectional flow area [L2] b = empirical coefficient to power law relationship c = coefficient for submerged inlet control head-discharge equation C = boundary roughness coefficient Cc = boundary roughness coefficient (Chezy’s Equation) Cd = discharge coefficient D = interior height of culvert barrel for embedded culverts; culvert diameter for circular culverts [L] Dh = maximum horizontal culvert span (diameter for circular culverts) [L] Dr = representative particle diameter [L] f = hydraulic roughness coefficient (Darcy-Weisbach Equation) F = function of Fr = Froude number Fx = force acting in horizontal (x) direction [F] g = acceleration due to gravity [L/t2] h = flow depth [L] hmeasured = measured flow depth [L] hcalculated = calculated flow depth with GVF profile calculation [L] haverage = average of measured flow depth (ymeasured) [L] H = total head upstream of the flow measurement V-notched weir Hc = total head at critical depth (dc+V2c/2g) [L] He = culvert entrance head loss [L] Ho = culvert exit loss, energy per unit volume [L] Hw = total energy upstream of a culvert relative to the culvert invert (or streambed for a buried-invert culvert) at the inlet [L] Notation

82 Hwi = headwater depth upstream of a culvert relative to the culvert invert (or streambed for a buried-invert culvert) at the inlet [L] k = equivalent roughness height [L] ke = entrance loss coefficient ko = exit loss coefficient ks = pipe wall roughness height [L] K = coefficient for unsubmerged inlet control equations Kn = 1 for SI units and = 3.281(1-x) (=1.49 when x′ = ²⁄³) for ES units Ku = unit conversion constant for inlet control equations 1.0, ES (1.811, SI) L = length m = side wall slope (horizontal to vertical) of trapezoidal channel cross-section M = exponent in unsubmerged inlet control equations n = Manning’s n hydraulic roughness coefficient n = boundary roughness coefficient (Manning’s Equation) naverage = average n from experimental data nc = equivalent n value for Chezy and Darcy-Weisbach equations ne = composite Manning’s n neq = boundary roughness coefficient (dependent on x in Eqn. (6)) ni = component n values of individual boundary roughness materials nopt = equivalent n value where x of Equation 6 is optimized samples = number of data points sampled which contribute to the RMS P = wetted perimeter [L] Pi = component wetted perimeter resulting from the partitioning of a composite-channel into subareas between the boundary roughness materials [L] P1 = hydrostatic pressure at location 1 (see Figure 4-2) [F/L2] P2 = hydrostatic pressure at location 2 (see Figure 4-2) [F/L2] PE = predictive error [%] Q = volumetric flow rate [L3/t] r2 = coefficient of determination Re = Reynolds number Rh = hydraulic radius (Aflow/P) [L] Rhi = component hydraulic radius (Ai/Pi) [L] RMS = Root Mean Square [%] So = slope of culvert barrel [L/L] Se = the energy grade line slope (friction slope) t = time T = width of trapezoidal channel at water surface [L] Tw = tailwater depth, measured relative to culvert outlet invert [L] U = shear velocity V = mean velocity of flow [L/t] V = mean channel velocity [L/t] V = shear velocity = (gRhS)1/2 [L/t] Vch = average channel flow velocity downstream of a culvert outlet [L/t] Vp = average culvert flow velocity [L/t] x = primary flow direction coordinate

83 x′ = exponent applied to Rh in basic uniform-flow equation y = flow depth y′ = exponent applied to S in basic uniform-flow equation yaverage = average channel profile flow depth [L] ycalculated = flow depth calculated by the GVF computer program ymeasured = measured flow depth yn = normal depth [L] Y = constant for submerged inlet control equation Dz = elevation difference between the inverts of the culvert outlet and channel [L] g = fluid specific weight [F/L3] q = angle of the V-notch r = fluid density [m/L3] n = kinematic viscosity [L2/t]