§ 5.5.2. Minor Losses
From the point at which stormwater enters the drainage system at the inlet until it discharges at the outlet, it encounters a variety of hydraulic structures such as manholes, bends, enlargements, contractions and other transitions. These structures will cause headlosses which are called "minor headlosses."
Table 5-3
Minor Loss Methodology and Coefficients
Minor Loss Calculations Case Reference Figure Description Headloss Method Coefficient, K Reference 1 Exit Losses H o =K[(V o /2g) - (Vd2/2g)] where H o = exit loss; V o = average outlet velocity; V d = channel velocity downstream of outlet in the direction of the pipe flow; and g = acceleration due to gravity, 32.2 ft/s . 1.0 Equation 7-4, FHWA Hydraulic Engineering Circular No. 22, September 2009. 2 Manhole or junction on trunk line with or without a change in flow direction (applicable only when all of the following conditions are met: the deflection angle is less than 90 degrees, there is only one pipe flowing into the manhole and one pipe flowing out, the inflow and outflow pipes are of equal diameter, and there is no sudden drop in elevation between the inflow pipe and the outflow pipe. When any of these conditions are not met, use the methodology required below for Case 3.) H = K(V /2g) Use loss coefficient determined from Figure 5-1. Use Curve A if the bottom shaping is provided in the manhole. Use Curve B if the manhole does not have bottom shaping. Reference: Urban Storm Drainage Criteria Manual, Volume 1, Prepared for the Urban Drainage and Flood Control District, Denver Colorado, June 2001, Revised April 2008. 3 All inlets, manholes and junction boxes not covered by Case 2. FHWA Inlet and Access Hole Energy Loss Method (FHWA Hydraulic Engineering Circular No. 22, latest edition). Use of the method shall account for energy losses at manholes having either straight or angled runs, and shall account for all branch laterals connected to the manhole. Adjustments shall be made for angled flows, plunging flows, and benching within the structure. Determine the hydraulic grade line elevation by subtracting the velocity head from the energy grade line elevation. FHWA Hydraulic Engineering Circular No. 22, latest edition. 4 Wye Connection or cut-in at any angle (No junction box or manhole is present) Where no junction box or manhole is present, use the momentum equation (FHWA Junction Loss Method): H j ={[(Q o V o )- (Q i +V i- )-(Q l V l cosTHETA j )]/ [0.5g(A o +A i )]}+h i -h o where the terms are as defined in FHWA Hydraulic Engineering Circular No. 22. FHWA Hydraulic Engineering Circular No. 22, latest edition. 5 Single-angle mitered bend or elbow. H = K(V /2g) Use loss coefficient determined from Figure 5-2. Reference: U.S. Bureau of Reclamation, Design of Small Canal Structures, Denver, Colorado, 1978. 6 Loss Coefficients for Bends H = K(V /2g) Reference: Normann, J.M., R.J. Houghtalen, and W.J. Johnston, 2001 (Revised May 2005), Hydraulic Design of Highway Culverts, Second edition, Hydraulic Design Series No. 5, Washington, D.C., Federal Highway Administration (FHWA). 90-degree bend where radius of bend/ equivalent diameter of pipe = 1 0.50 90-degree bend where radius of bend/ equivalent diameter of pipe = 2 0.30 90-degree bend where radius of bend / equivalent diameter of pipe = 4 0.25 90-degree bend where radius of bend / equivalent diameter of pipe = 6 0.15 90-degree bend where radius of bend / equivalent diameter of pipe = 8 0.15 45-degree bend where radius of bend / equivalent diameter of pipe = 1 0.37 45-degree bend where radius of bend / equivalent diameter of pipe = 2 0.22 45-degree bend where radius of bend / equivalent diameter of pipe = 4 0.19 45-degree bend where radius of bend / equivalent diameter of pipe = 6 0.11 45-degree bend where radius of bend / equivalent diameter of pipe = 8 0.11 22.5-degree bend where radius of bend / equivalent diameter of pipe = 1 0.25 22.5-degree bend where radius of bend / equivalent diameter of pipe = 2 0.15 22.5-degree bend where radius of bend / equivalent diameter of pipe = 4 0.12 22.5-degree bend where radius of bend / equivalent diameter of pipe = 6 0.08 22.5-degree bend where radius of bend / equivalent diameter of pipe = 8 0.08 7 Conduit placed to create a continuous curve H = K(V /2g) Use loss coefficient determined from Figure 5-1. Reference: Urban Storm Drainage Criteria Manual, Volume 1, Prepared for the Urban Drainage and Flood Control District, Denver, Colorado, June 2001, Revised April 2008. C.
Transition Losses. The headlosses resulting from sudden and gradual changes in the cross section or flow direction are included in this category. Four (4) transition losses are discussed here.
1.
Sudden Enlargement. Table 5-4 shows the coefficients used in the different cases for headlosses due to a sudden enlargement.
2.
Gradual Enlargement. Table 5-5 shows the coefficients for calculating the headlosses based on the angle of the cone transition.
3.
Sudden Contraction. Table 5-6 illustrates the values of coefficients in determining the headloss due to a sudden contraction.
4.
Gradual Contraction. The headlosses due to a gradual contraction are determined by the following equation with a constant headloss coefficient.
H gc = 0.04 V /2g (Eq. 5-4)
Where,
V = velocity for smaller pipe.
Table 5-4
Values of K for Determining Loss of Head Due to Sudden
Enlargement in Pipes, from the Formula H = K (V /2g)
d 1 /d 2 Velocity, V, fps 2 3 4 5 6 7 8 10 12 15 20 1.2 .11 .10 .10 .10 .10 .10 .09 .09 .09 .09 .09 1.4 .26 .26 .25 .24 .24 .24 .24 .23 .23 .22 .22 1.6 .40 .39 .38 .37 .37 .36 .36 .35 .35 .34 .33 1.8 .51 .49 .48 .47 .47 .46 .46 .45 .44 .43 .42 2.0 .60 .58 .56 .55 .55 .54 .53 .52 .52 .51 .50 2.5 .74 .72 .70 .69 .68 .67 .66 .65 .64 .63 .62 3.0 .83 .80 .78 .77 .76 .75 .74 .73 .72 .70 .69 4.0 .92 .89 .87 .85 .84 .83 .82 .80 .79 .78 .76 5.0 .96 .93 .91 .89 .88 .87 .86 .84 .83 .82 .80 10.0>10.0 1.00
1.00.99
1.00.96
.98.95
.96.93
.95.92
.94.91
.93.89
.91.88
.90.86
.88.84
.86V = velocity in smaller pipe
d 2 /d 1 = ratio of diameter of larger pipe to diameter of smaller pipeSource: Brater, E.F. and H.W. King. Handbook of Hydraulics . Table 5-5
Values of K for Determining Loss of Head Due to Gradual
Enlargement in Pipes from the Formula H = K (V /2g)d 2 /d 1 Angle of cone* 2° 4° 6° 8° 10° 15° 20° 25° 30° 35° 40° 45° 50° 60° 1.1 .01 .01 .01 .02 .03 .05 .10 .13 .16 .18 .19 .20 .21 .23 1.2 .02 .02 .02 .03 .04 .09 .16 .21 .25 .29 .31 .33 .35 .37 1.4 .02 .03 .03 .04 .06 .12 .23 .30 .36 .41 .44 .47 .50 .53 1.6 .03 .03 .04 .05 .07 .14 .26 .35 .42 .47 .51 .54 .57 .61 1.8 .03 .04 .04 .05 .07 .15 .28 .37 .44 .50 .54 .58 .61 .65 2.0 .03 .04 .04 .05 .07 .16 .29 .38 .46 .52 .56 .60 .63 .68 2.5 .03 .04 .04 .05 .08 .16 .30 .39 .48 .54 .58 .62 .65 .70 3.0>3.0 .03
.03.04
.04.04
.04.05
.06.08
.08.16
.16.31
.31.40
.40.48
.49.55
.56.59
.60.63
.64.66
.67.71
.72* Angle of cone is twice the angle between the axis of the cone and its side. V = velocity in smaller pipe. d 2 /d 1 = ratio of diameter of larger pipe to diameter of smaller pipe. Source: Brater, E.F. and H.W. King. Handbook of Hydraulics . Table 5-6
Values of K for Determining Loss of Head Due to Sudden
Contraction in Pipe From the Formula H = K (V2/2g)d 2 /d 1 Velocity, V in feet per second 2 3 4 5 6 7 8 10 12 15 20 1.1 .03 .04 .04 .04 .04 .04 .04 .04 .04 .04 .05 1.2 .07 .07 .07 .07 .07 .07 .07 .08 .08 .08 .09 1.4 .17 .17 .17 .17 .17 .17 .17 .18 .18 .18 .18 1.6 .26 .26 .26 .26 .26 .26 .26 .26 .26 .25 .25 1.8 .34 .34 .34 .34 .34 .34 .33 .33 .32 .32 .31 2.0 .38 .38 .37 .37 .37 .37 .36 .36 .35 .34 .33 2.2 .40 .40 .40 .39 .39 .39 .39 .38 .37 .37 .35 2.5 .42 .42 .42 .41 .41 .41 .40 .40 .39 .38 .37 3.0 .44 .44 .44 .43 .43 .43 .42 .42 .41 .40 .39 4.0 .47 .46 .46 .46 .45 .45 .45 .44 .43 .42 .41 5.0 .48 .48 .47 .47 .47 .46 .46 .45 .45 .44 .42 10.0>10.0 .49
.49.48
.49.48
.48.48
.48.48
.48.47
.47.47
.47.46
.47.46
.46.45
.45.43
.44V = velocity in smaller pipe d 2 /d 1 = ratio of diameter of larger pipe to diameter of smaller pipe Source: Brater, E.F. and H.W. King. Handbook of Hydraulics .