Hydrology (thủy văn cơ sở)

HYDR 3026 Reference Manual Spring 2016 Page of 35 HYDR 3026 Formula Sheet Conversions 12 inches = foot 5,280 feet = mile 43,560 square feet = acre 640 acres = square mile 7.48 gallons = cubic foot 3,600 seconds = hour 86,400 seconds = day Manning’s Equation Full form of Manning’s Equation for velocity and flow v k 0.66 0.5 Rh S n Q k ARh0.66 S 0.5 n where: v = velocity of uniform flow (m/sec or ft/sec) Q = flowrate (m3/sec or ft3/sec) k = 1.0 (metric) or 1.49 (US customary units) n = Manning’s roughness coefficient(-) Rh = hydraulic radius (m or ft) = A/WP A = cross-sectional area of flow (m2 or ft2) WP = wetted perimeter of stream (m or ft) S = slope of the energy gradeline(slope of ground surface at uniform flow) (m/m or ft/ft) Short form of Manning’s Equation for Sheet Flow velocity (see Sheet Flow Manning’s n Table) v  kS 0.5 where: v = velocity of uniform flow (ft/sec) 1.49 0.66 Rh (not the same as the “k” in full form of Manning’s equation above) k= n S = slope of the energy gradeline(and ground surface at uniform flow) (m/m or ft/ft) n = Manning’s roughness coefficient for sheet flow (see Table 15-1) Page of 35 Flow Equations leader& vertical drains d  0.6Qd0.377 where: d = internal diameter of drain (in) Qd = capacity of drain (gal/min or gpm) horizontal drain d  0.53S 0.188Qd0.377 where: d = internal diameter of drain (in) S = drain slope (in/ft) Qd = capacity of drain (gal/min or gpm) Orifice equation (fully submerged opening) q  C d A gh where: q = flowrate through the orifice (ft3/sec or cfs) Cd = coefficient of discharge (typically 0.65) A = area of orifice (ft2) g = gravitational constant (32.2 ft/sec2) h = head above the center of the orifice (ft) suppressed weir equation (full width of channel or small h vs L ) q  C w Lh1.5 where: q = flowrate over weir(ft3/sec or cfs) Cw = coefficient of discharge (typically 3.0) L = length of weir (ft) h = head above the crest of the weir (ft) contracted weir equation (partial width of channel) q  C w L  0.2hh1.5 where: q = flowrate over the weir (ft3/sec or cfs) Cw = coefficient of weir (typically 3.3) L = length of weir (ft) h = head above the crest of the weir (ft) slotted drain equation(acting as an orifice) q  C d LW 2gd  0.5 where: q = discharge rate (ft3/sec or cfs) Cd = coefficient of discharge (typically 0.8) L = length of slotted drain (ft) W = width of slotted drain (ft) g = gravitational constant (32.2 ft/sec2) d = depth of water above the slotted drain (ft) Page of 35 half circle channel q 1.25 2.125 0.54 0.5 d D S n  D    D    T  2       d          0.5 where: q = discharge rate (ft3/sec or cfs) n = Manning’s roughness coefficient for channels (-) d = depth of water in channel (ft) D = diameter of channel (ft) T = top width of water (ft) S = slope of energy gradeline (and at uniform flow, the channel bottom) (ft/ft) triangular channel q   0.47 z d 2.67 S 0.5 n qn   d  0.5   0.47 zS  0.375 T  zd where: q = discharge rate (ft3/sec or cfs) n = Manning’s roughness coefficient for channels (-) d = depth of water in channel (ft) z = inverse of cross slope (ft/ft) T = top width of water (ft) S = slope of energy gradeline (and at uniform flow, the channel bottom) (ft/ft) Page of 35 Time of Concentration Equations ALSO SEE MANNING’S EQUATION FOR SHEET FLOW Lag method(for watersheds where overland flow predominates) L0.8 S  1 Tc  1,140Y 0.5 0.7 0.7  1000  Tc  0.0000877 L    Y 0.5  CN  or 0.8 where: Tc = time of concentration (hr) L = flow length (ft) S = maximum potential retention = 1000 1000  10   10 ' CN cn cn’ = retardance factor ~ CN CN = average watershed curve number Y = average watershed slope (%) Sheet flow- kinematic wave formula with “i”(remember - we are trying to determine tc to determine “i”) Tt  0.938  nL    i 0.4  S 0.5  0.6 where: Tt = travel time for sheet flow (min) i = intensity (in/hr) n = Manning’s roughness coefficient for sheet flow (see Table 15-1) L = distance of travel for sheet flow (ft) S = slope of the energy gradeline and ground surface at uniform flow (ft/ft) Sheet flow - kinematic wave formula with P2-24 Tt  0.007  nL    P20.524  S 0.5  0.8 where: Tt = travel time for sheet flow (hr) P2-24= precipitation or rainfall (in) n = Manning’s roughness coefficient for sheet flow (see Table 15-1) L = distance of travel for sheet flow (ft) S = slope of the energy gradeline(and ground surface at uniform flow) (ft/ft) Watershed Length very rough estimation L  209A 0.6 where: L = total distance of travel in watershed (ft) A = watershed area (acres) Page of 35 Models for estimating detention pond storage Rational Method Vst  0.08264 q p a  q pb  t ca Natural Storage Vst  0.0833 Qa  Qb A Baker Vst  0.0833 1    Qa A Wycoff& Singh Vst  0.107 Qa A 1    Abt&Grigg 1 m  Vst  0.08264   q p a t c a 1      SCS TR-55 regions II & III Vst  0.0833 0.682  1.43  1.64  0.804 Qa A 0.753 region I & IA   Tb  t  p a      0.411   Vst  0.0833 0.66  1.76  1.96  0.73 Qa A where: A = watershed area (acres) m = (Tb – tp)/tp Qa = depth of runoff after development (in) Qb = depth of runoff before development (in) qp-a = peak flowrate after development (cfs) qp-b = peak flowrate before development (cfs) = time of start of runoff to peak = time of start of runoff to peak = 0.6tc tc-a = time of concentration after development (end of rainfall to point of inflection on recession leg) (hrs) tc-b= time of concentration before development (end of rainfall to point of inflection on recession leg) (hrs) Tb = total time of runoff (hrs) Vst = volume of storage (acre-ft)  = ration of qp-b/qp-a Coefficients for the SCS Detention-Volume Method SCS Rainfall Distribution Type I or IA II or III C0 0.660 0.682 C1 -1.760 -1.430 C2 1.960 1.640 C3 -0.730 -0.804 Page of 35 Statistics exceedence probability Weibull formula, Pi  i n 1 Hazen formula, Pi  2i  2n Cunnane, Pi  i  0.4 n  0.2 return period = sample mean = X  T Pi n  Xi n i 1   n standard deviation = S    Xi  X  n  i 1 n skew = g   n X i  X i 1     0.5  n  1n  2S where: Pi = plotting position or probability of an event of this size or larger occurring n = number of events (random variables) in sample g = skew i = rank of an event S = standard deviation T = return period X = value of random variable Page of 35 Peak Runoff Rational Method Q p  CiA where: Qp = peak discharge (cfs) C = Rational Method Coefficient of Runoff i = intensity (in/hr) A = watershed area (acres) SCS Method q p  qu AQ Q P24  0.2S 2 P24  0.8S   1000  S    10 I a  0.2S  CN  where: CN = SCS curve number S = total retention (in) Ia = initial abstraction P24 = 24 hour precipitation at desired frequency (in) Q = total runoff (in) A = watershed area (mi2) qu = unit peak discharge (csm/in) (see peak discharge graphs) qp = peak discharge (cfs) Page of 35 Detention Pond Sizing Equations A0 = area of orifice = q aj C d g E j  E0  0.5H  0.5 C = coefficient = 0.456 + 0.047 X – 0.0024 X2 + 0.00006 X3 Cd = coefficient of discharge for an orifice typically equal to 0.6 Cw = weir coefficient, typically 3.0 d = diameter of outlet pipe (in) = D*12 D = diameter of outlet pipe (ft) = (C)qaj0.5/((E0-Ec)0.25) (for multi-stage riser, qaj = highest stage event) ds = Vs = depth of active storage (over entire watershed) (in) = RsQa Ec = elevation of center of discharge pipe (ft) Ei = elevation of invert of discharge pipe (ft) = Ec – 0.5D Ej = elevation of water surface for the “j” storm (ft) Eo = elevation of bottom of lowest opening (top of dead storage or bottom of pond) (ft) Et = elevation of tailwater depth (in this class = zero, but in real life – probably NOT = zero) (ft) Ho = height of orifice (ft) = Ao/Wo(the orifice must be submerged) Kp = coefficient of headloss + friction factor = 5087 n2d-1.33 or see Kp table L = length of discharge pipe (ft) Lw1 = length of weir for first stage (ft) = qaj/(Cw(Ej-E0)1.5) Lw2 = required length of weir for second stage (or higher stage) (taking into account the stage one opening) (ft) = (qpb2 – q02)/((E2 – E1)1.5) n = Manning’s roughness coefficient for channels (see Manning’s “n” table for channels) Rq = peak discharge ratio (-) == qpb/qpa Rs = storage ratio (-) = Vs/Qa = C0 + C1Rq + C2Rq2) + C3(Rq3) = C0 + C1 + C22) + C3 (3) (see section above - Models for estimating detention pond storage for C values) qaj = allowed flow from orifice (cfs) (typically pre-development flow of storm “j”) q01 = flow from orifice at first stage (cfs) = C d g AO E1  E0  0.5H 0.5 q02 = flow from orifice at second stage (cfs) = C d g AO E  E0  0.5H 0.5 Qa = depth of total runoff after development (over entire watershed) (in) (SCS Method) Qb = depth of total runoff before development (over entire watershed) (in) (SCS Method) Vd = dead storage volume (acre-ft) Vs = ds = active storage volume (in) Vst = active storage volume (acre-ft) Vt = total volume of pond (Vs + Vd) (acre-ft) Wo = width of orifice (ft) =Ao/Ho =~ 0.75D (this is an approximation – orifice must operate as an orifice) X = KpL (ft)  = qp ratio = Rq = qpb/qpa See figures on next page Page of 35 E1 E1 E0 H0 A0 E0 Lw/2 W0 D D EC Ei EC Ei Single Stage Riser with either a weir or an orifice E2 E1 E2 E1 Lw2 D H0 W0 EC E0 Lw2 Lw1 EC Ei Ei E0 D Two Stage Riser (low stage orifice/high stage weir) and (low stage weir and high stage weir) Kp Table (entrance loss coefficient and friction factor coefficient) Pipe Diameter RCP CMP (in) (n = 0.013) (n = 0.024) 24 0.0124 0.0423 27 0.01061 0.0362 30 0.00922 0.0314 36 0.00723 0.0246 42 0.00589 0.0201 48 0.00493 0.0168 54 0.00421 0.0144 60 0.00366 0.0125 Page 10 of 35 Design Frequencies vs type of roadway and average daily traffic Table from Arkansas Highway & Transportation Department CROSS DRAINS Interstate Projects Primary Projects Federal Aid Urban Projects Secondary Projects Non-Federal Aid Projects (area < sq.mi and ADT < 750) (area > sq.mi or ADT > 750) STORM SEWERS Interstate and/or Interstate Type Project Other Federal Aid Projects Non-Federal Aid Projects Design Freq (years) 50 50 25 25 10 25 50 10 Page 21 of 35 Peak Flow Figures and Table Page 22 of 35 Page 23 of 35 Page 24 of 35 Page 25 of 35 Runoff Coefficients for the Rational Formula versus Hydrologic Soil Group (A, B, C, D) and Slope Land Use A B C D 0-2% 2-6% >6% 0-2% 2-6% >6% 0-2% 2-6% >6% 0-2% 2-6% >6% 0.08a 0.13 0.16 0.14b 0.18 0.22 Pasture 0.12 0.20 0.30 0.15 0.25 0.37 Meadow 0.10 0.16 0.25 0.14 0.22 0.30 Forest 0.05 0.08 0.11 0.08 0.11 0.14 Res 1/8 acre lot 0.25 0.28 0.31 0.33 0.37 0.40 Res 1/4 acre lot 0.22 0.26 0.29 0.30 0.34 0.37 Res 1/3 acre lot 0.19 0.23 0.26 0.28 0.32 0.35 Res 1/2 acre lot 0.16 0.20 0.24 0.25 0.29 0.32 Res acre lot 0.14 0.19 0.22 0.22 0.26 0.29 Industrial 0.67 0.68 0.68 0.85 0.85 0.86 Commercial 0.71 0.71 0.72 0.88 0.88 0.89 Streets 0.70 0.71 0.72 0.76 0.77 0.79 Open space 0.05 0.10 0.14 0.11 0.16 0.20 Parking 0.85 0.86 0.87 0.95 0.96 0.97 a - for frequencies less than 25 years, Cultivated land 0.11 0.15 0.21 0.14 0.19 0.26 0.18 0.16 0.21 0.28 0.20 0.25 0.34 0.24 0.18 0.28 0.37 0.24 0.34 0.44 0.30 0.23 0.34 0.45 0.30 0.42 0.52 0.37 0.14 0.22 0.30 0.20 0.28 0.36 0.24 0.20 0.28 0.37 0.26 0.35 0.44 0.30 0.08 0.11 0.14 0.10 0.13 0.16 0.12 0.10 0.14 0.18 0.12 0.16 0.20 0.15 0.27 0.30 0.35 0.30 0.33 0.38 0.33 0.35 0.39 0.44 0.38 0.42 0.49 0.41 0.24 0.29 0.33 0.27 0.31 0.36 0.30 0.33 0.37 0.42 0.36 0.40 0.47 0.38 0.22 0.26 0.30 0.25 0.29 0.34 0.28 0.30 0.35 0.39 0.33 0.38 0.45 0.36 0.19 0.23 0.28 0.22 0.27 0.32 0.26 0.28 0.32 0.36 0.31 0.35 0.42 0.34 0.17 0.21 0.26 0.20 0.25 0.31 0.24 0.24 0.28 0.34 0.28 0.32 0.40 0.31 0.68 0.68 0.69 0.68 0.69 0.69 0.69 0.85 0.86 0.86 0.86 0.86 0.87 0.86 0.71 0.72 0.72 0.72 0.72 0.72 0.72 0.89 0.89 0.89 0.89 0.89 0.90 0.89 0.71 0.72 0.74 0.72 0.73 0.76 0.73 0.80 0.82 0.84 0.84 0.85 0.89 0.89 0.08 0.13 0.19 0.12 0.17 0.24 0.16 0.14 0.19 0.26 0.18 0.23 0.32 0.22 0.85 0.86 0.87 0.85 0.86 0.87 0.85 0.95 0.96 0.97 0.95 0.96 0.97 0.95 b - for frequencies equal/greater than 25 years 0.23 0.29 0.40 0.50 0.30 0.40 0.16 0.20 0.36 0.45 0.34 0.42 0.32 0.40 0.30 0.38 0.29 0.35 0.69 0.86 0.72 0.89 0.75 0.91 0.21 0.27 0.86 0.96 0.31 0.41 0.50 0.62 0.40 0.50 0.20 0.25 0.42 0.54 0.40 0.52 0.39 0.50 0.37 0.48 0.35 0.46 0.70 0.88 0.72 0.90 0.78 0.95 0.28 0.39 0.87 0.97 Page 26 of 35 Runoff Coefficients for the Rational Method Description of Area Business Downtown Neighborhood Residential Single-family Multi-units, detached Multi-units, attached Residential (surburban) Apartments Industrial Light Heavy Parks, cemeteries Playgounds Railroad yard Unimproved Pavement Asphaltic & Concrete Brick Roofs Lawns, sandy soil Flat, 2% Average, to 7% Steep, >7% Lawns, heavy soil Flat, 2% Average, to 7% Steep, >7% Range of Runoff Coefficients Recommended Coefficient 0.70 - 0.95 0.50 - 0.70 0.85 0.60 0.30 - 0.50 0.40 - 0.60 0.60 - 0.75 0.25 - 0.40 0.50 - 0.70 0.40 0.50 0.70 0.35 0.60 0.50 - 0.80 0.60 - 0.90 0.10 - 0.25 0.20 - 0.35 0.20 - 0.35 0.10 - 0.30 0.65 0.75 0.20 0.30 0.30 0.20 0.70 - 0.95 0.75 - 0.85 0.75 - 0.95 0.85 0.80 0.85 0.05 - 0.10 0.10 - 0.15 0.15 - 0.2 0.08 0.13 0.18 0.13 - 0.17 0.18 - 0.22 0.25 - 0.35 0.15 0.20 0.30 Page 27 of 35 Recommended Allowable Spread for Roadways (FHWA) Page 28 of 35 SCS Dimensionless Unit Hydrograph Time Discharge Ratio Ratio t/tp q/qp 0.0 0.000 0.1 0.030 0.2 0.100 0.3 0.190 0.4 0.310 0.5 0.470 0.6 0.660 0.7 0.820 0.8 0.930 0.9 0.990 1.0 1.000 1.1 0.990 1.2 0.930 1.3 0.860 1.4 0.780 1.5 0.680 1.6 0.560 1.7 0.460 1.8 0.390 1.9 0.330 2.0 0.280 2.2 0.207 2.4 0.147 2.6 0.107 2.8 0.077 3.0 0.055 3.2 0.040 3.4 0.029 3.6 0.021 3.8 0.015 4.0 0.011 4.5 0.005 5.0 0.000 Mass Curve Ratio Qa/Q 0.000 0.001 0.006 0.012 0.035 0.065 0.107 0.163 0.228 0.300 0.375 0.450 0.522 0.589 0.650 0.700 0.751 0.790 0.822 0.849 0.871 0.908 0.934 0.947 0.963 0.977 0.984 0.989 0.993 0.995 0.997 0.999 1.000 Page 29 of 35 Standardized Variant K values for given skews (g) and probabilities (P) (plotting positions) Page 30 of 35 Page 31 of 35 Page 32 of 35 Page 33 of 35 Page 34 of 35 Page 35 of 35