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Stormwater Conveyance Design 2
John Reimer City of Madison Engineering Department
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Flow Routing Q t Procedure to determine the flow hydrograph at a point on a watershed from a known hydrograph upstream As the hydrograph travels, it attenuates gets delayed Q t Q t Q t
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Why route flows? Q t Account for changes in flow hydrograph as a flood wave passes downstream This helps in Accounting for storages Studying the attenuation of flood peaks
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Lumped flow routing Reservoir Routing (Modified Puls)
Storage is nonlinear function of Q Streamflow Routing (Muskingum method) Storage is linear function of I and Q
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Why do we need a pond to serve the development?
RECALL: Urbanization Runoff Hydrograph Post-development Discharge Pre-development Pond Outlet Time
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Reservoir Storage Storage Required S = ½ Qd tb - ½ Qu tb
Triangular Hydrograph Method Post-development Post-development (Qd) Storage Required Storage Required Discharge Discharge Pre-development Pre-development (Qu) Time Time t tb Storage Required S = ½ Qd tb - ½ Qu tb S = ½ tb (Qd-Qu)
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Reservoir Routing
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Reservoir Routing Procedure for calculating outflow hydrograph Q(t) from a reservoir with horizontal water surface, given its inflow hydrograph I(t) and storage-outflow relationship
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Reservoir Storage S(t) = Volume of water stored at t (cfs.hrs)
I(t) = Inflow Rate O(t) = Outflow Rate S(t) If we integrate to a given t Discharge Time t Water in Storage Total Inflow Total Outflow When: I(t) > O(t), dS/dt> Filling I(t) < O(t), dS/dt< Emptying I(t) = O(t)
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Reservoir Routing Modified puls Method (Storage Indication Method)
Continuity Equation: Inflow Finite difference form: Outflow t0 t1 Move known terms to left: Repeat for next time step:
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Example Given the following storage-outflow relationship and inflow hydrograph, calculate the outflow hydrograph. (Use 10-minute routing interval). Water Level (ft) Outflow Storage (ac-ft) 1 15 2 32 3 55 4 90 5 125 6 158 7 185 7.5 8 210 10.5 9 230 12 10 250 13.5 11 270 20 290 22
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Stage – Storage Relationship
Based on Pond Topography/Shape Water Level (ft) Outflow Storage (ac-ft) 1 15 2 32 3 55 4 90 5 125 6 158 7 185 7.5 8 210 10.5 9 230 12 10 250 13.5 11 270 20 290 22
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Reservoir routing as a computation of mass balance
For a reservoir the outflow is uniquely controlled by the water depth (or stage) of the reservoir pool. Also, the reservoir storage is a single-value function of the stage. As a result, given a stage the reservoir storage and outflow can be uniquely determined, if the stage~storage and stage~outflow relationships are known.
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Unknown Recall: CREATE LOOKUP TABLE 10 minutes Water Level (ft)
Outflow Storage (ac-ft) 1 15 2 32 3 55 4 90 5 125 6 158 7 185 7.5 8 210 10.5 9 230 12 10 250 13.5 11 270 20 290 22 Storage (cfs-min) 2S/delta t +O 726 160.2 1452 322.4 2178 490.6 2904 670.8 3630 851 4356 1029.2 5445 1274 7623 1734.6 8712 1972.4 9801 2210.2 14520 3174 15972 3484.4
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Computations Time Inflow 10 60 20 120 30 180 40 240 50 300 360 70 320
10 60 20 120 30 180 40 240 50 300 360 70 320 80 280 90 100 200 110 160 130 140 150 170 190
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Computations Time Inflow 10 60 20 120 30 180 40 240 50 300 360 70 320
10 60 20 120 30 180 40 240 50 300 360 70 320 80 280 90 100 200 110 160 130 140 I1+I2 Outflow Storage (cfs-min) 2S/dt - O1 2S/dt -O1 + I1 + I2 WSE 0.00 60 0.37 180 6 272 49 229 1.42 300 22 1033 184 484 2.96 420 54 2151 376 796 4.70 540 114 3409 567 1107 6.32 660 167 4704 774 1434 7.35 680 194 6202 1047 1727 7.98 600 210 7586 1308 1908 8.73 520 225 8415 1459 1979 9.03 440 231 8740 1517 1957 8.94 360 8644 1500 1860 8.53 280 221 8197 1419 1699 7.92 200 208 7454 1283 1483 7.45 120 196 6432 1090 1210 6.74
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Computations Use Lookup Table Time Inflow 10 60 20 120 30 180 40 240
10 60 20 120 30 180 40 240 50 300 360 70 320 80 280 90 100 200 110 160 130 140 I1+I2 Outflow Storage (cfs-min) 2S/dt - O1 2S/dt -O1 + I1 + I2 WSE 0.00 60 0.37 180 6 272 49 229 1.42 300 22 1033 184 484 2.96 420 54 2151 376 796 4.70 540 114 3409 567 1107 6.32 660 167 4704 774 1434 7.35 680 194 6202 1047 1727 7.98 600 210 7586 1308 1908 8.73 520 225 8415 1459 1979 9.03 440 231 8740 1517 1957 8.94 360 8644 1500 1860 8.53 280 221 8197 1419 1699 7.92 200 208 7454 1283 1483 7.45 120 196 6432 1090 1210 6.74
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LOOKUP TABLE Water Level (ft) Outflow Storage (ac-ft) 1 15 2 32 3 55 4
1 15 2 32 3 55 4 90 5 125 6 158 7 185 7.5 8 210 10.5 9 230 12 10 250 13.5 11 270 20 290 22 Storage (cfs-min) 2S/delta t +O 726 160.2 1452 322.4 2178 490.6 2904 670.8 3630 851 4356 1029.2 5445 1274 7623 1734.6 8712 1972.4 9801 2210.2 14520 3174 15972 3484.4
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Computations Use Lookup Table Time Inflow 10 60 20 120 30 180 40 240
10 60 20 120 30 180 40 240 50 300 360 70 320 80 280 90 100 200 110 160 130 140 I1+I2 Outflow Storage (cfs-min) 2S/dt - O1 2S/dt -O1 + I1 + I2 WSE 0.00 60 0.37 180 6 272 49 229 1.42 300 22 1033 184 484 2.96 420 54 2151 376 796 4.70 540 114 3409 567 1107 6.32 660 167 4704 774 1434 7.35 680 194 6202 1047 1727 7.98 600 210 7586 1308 1908 8.73 520 225 8415 1459 1979 9.03 440 231 8740 1517 1957 8.94 360 8644 1500 1860 8.53 280 221 8197 1419 1699 7.92 200 208 7454 1283 1483 7.45 120 196 6432 1090 1210 6.74
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LOOKUP TABLE Water Level (ft) Outflow Storage (ac-ft) 1 15 2 32 3 55 4
1 15 2 32 3 55 4 90 5 125 6 158 7 185 7.5 8 210 10.5 9 230 12 10 250 13.5 11 270 20 290 22 Storage (cfs-min) 2S/delta t +O 726 160.2 1452 322.4 2178 490.6 2904 670.8 3630 851 4356 1029.2 5445 1274 7623 1734.6 8712 1972.4 9801 2210.2 14520 3174 15972 3484.4
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Computations dt=10 minutes Time Inflow 10 60 20 120 30 180 40 240 50
10 60 20 120 30 180 40 240 50 300 360 70 320 80 280 90 100 200 110 160 130 140 I1+I2 Outflow Storage (cfs-min) 2S/dt - O1 2S/dt -O1 + I1 + I2 WSE 0.00 60 0.37 180 6 272 49 229 1.42 300 22 1033 184 484 2.96 420 54 2151 376 796 4.70 540 114 3409 567 1107 6.32 660 167 4704 774 1434 7.35 680 194 6202 1047 1727 7.98 600 210 7586 1308 1908 8.73 520 225 8415 1459 1979 9.03 440 231 8740 1517 1957 8.94 360 8644 1500 1860 8.53 280 221 8197 1419 1699 7.92 200 208 7454 1283 1483 7.45 120 196 6432 1090 1210 6.74
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Computations dt=10 minutes Time Inflow 10 60 20 120 30 180 40 240 50
10 60 20 120 30 180 40 240 50 300 360 70 320 80 280 90 100 200 110 160 130 140 I1+I2 Outflow Storage (cfs-min) 2S/dt - O1 2S/dt -O1 + I1 + I2 WSE 0.00 60 0.37 180 6 272 49 229 1.42 300 22 1033 184 484 2.96 420 54 2151 376 796 4.70 540 114 3409 567 1107 6.32 660 167 4704 774 1434 7.35 680 194 6202 1047 1727 7.98 600 210 7586 1308 1908 8.73 520 225 8415 1459 1979 9.03 440 231 8740 1517 1957 8.94 360 8644 1500 1860 8.53 280 221 8197 1419 1699 7.92 200 208 7454 1283 1483 7.45 120 196 6432 1090 1210 6.74
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Computations Use Lookup Table Time Inflow 10 60 20 120 30 180 40 240
10 60 20 120 30 180 40 240 50 300 360 70 320 80 280 90 100 200 110 160 130 140 I1+I2 Outflow Storage (cfs-min) 2S/dt - O1 2S/dt -O1 + I1 + I2 WSE 0.00 60 0.37 180 6 272 49 229 1.42 300 22 1033 184 484 2.96 420 54 2151 376 796 4.70 540 114 3409 567 1107 6.32 660 167 4704 774 1434 7.35 680 194 6202 1047 1727 7.98 600 210 7586 1308 1908 8.73 520 225 8415 1459 1979 9.03 440 231 8740 1517 1957 8.94 360 8644 1500 1860 8.53 280 221 8197 1419 1699 7.92 200 208 7454 1283 1483 7.45 120 196 6432 1090 1210 6.74
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LOOKUP TABLE Water Level (ft) Outflow Storage (ac-ft) 1 15 2 32 3 55 4
1 15 2 32 3 55 4 90 5 125 6 158 7 185 7.5 8 210 10.5 9 230 12 10 250 13.5 11 270 20 290 22 Storage (cfs-min) 2S/delta t +O 726 160.2 1452 322.4 2178 490.6 2904 670.8 3630 851 4356 1029.2 5445 1274 7623 1734.6 8712 1972.4 9801 2210.2 14520 3174 15972 3484.4
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Inflow/Outflow Time Inflow 10 60 20 120 30 180 40 240 50 300 360 70
10 60 20 120 30 180 40 240 50 300 360 70 320 80 280 90 100 200 110 160 130 140 Outflow 6 22 54 114 167 194 210 225 231 229 221 208 196
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Detention Storage Volume
TR-55, Chapter 6 (SCS, 1986) Vs=Vr(C0+C1(qo/qi)+C2(qo/qi)2+C3(qo/qi) 3) Vs=Required Storage Volume qo=Pre-development peak (desired outflow) qi=Post-development peak (inflow peak) Vr=Post-development runoff volume C0=0.682 C1=-1.43 C2=1.64 C3=-0.804 Type II and Type III Storms
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Outlet Structure Types
Categorized into three groups: Orifice Type Weir Type Sharp-crested Broad-crested V-notch Riser-pipe structures
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Orifice Circular or rectangular opening of a prescribed shape and size. Flow rate depends on the height of water above the opening and the size and edge treatment of the orifice Q=CdA(2gh)0.5 Q=orifice flow discharge Cd=coefficient of discharge (0.6 for square edge) A=cross-sectional area of orifice g=acceleration due to gravity h=effective head on orifice from the center of orifice to the water surface
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Sharp/Broad Crested Weir
A weir is defined as a regular obstruction across a channel section over which flow takes place It may be a vertical flat plate with a sharpened upper edge (Sharp Crested) It may have a solid broad section of concrete or ther material (Broad Crested) Sharp Crested: Q=(2/3) Cd (2g)1/2 L H3/2 Broad Crested: Q=(0.385) Cd (2g)1/2 L H3/2 Q=weir flow discharge Cd=weir discharge coefficient ( for sharp, for broad) L=weir length H=water depth above crest
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V-notch Weir Suitable for low discharges, because the head increases more rapidly on a triangular section Q=(8/15) Cd (2g)1/2 tan(q/2) H5/2 Q=weir flow discharge Cd=weir discharge coefficient (~0.6) H=head on apex of notch
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Channel Routing (Muskingum Method)
Wedge storage: Advancing Flood Wave I > Q Wedge Prism K = travel time of peak through the reach X = weight on inflow versus outflow (0 ≤ X ≤ 0.5) X = 0 Reservoir, storage depends on outflow, no wedge X = Natural stream Wedge Receding Flood Wave Q > I Prism
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Estimating K and X The Muskingum K is usually estimated from the travel time for a flood wave through the reach. This requires two flow gages with frequent data collection, one at the top and one at the bottom of single channel reaches. If they are not available, X averages 0.2 to 0.3 for a natural stream. If the two hydrographs are available , K and X can be better estimated. Storage S is plotted against the weighted discharge XI + (1-X)Q for several values of x. Since Muskingum method assumes this is a straight line, the straightest is x. Then K can be calculated from
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Channel Routing Muskingum Method (Cont.)
Recall: Rearrange: If I, K and X are known, Q(t) can be calculated using above equations
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Channel Routing Example
Given: Inflow hydrograph K = 25 min, X = 0.15, Dt = 10 min, Initial Q = 85 cfs Find: Outflow hydrograph using Muskingum routing method Channel Routing Detention Pond Routing (Previous Example)
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Channel Routing Example
Pond Outflow (Inflow to Channel) Channel Routing Example Given: Inflow hydrograph K = 25 min, X = 0.15, Dt = 10 min, Initial Q = 85 cfs Find: Outflow hydrograph using Muskingum routing method Time Inflow (min) (cfs) 10 20 6 30 22 40 54 50 114 60 167 70 194 80 210 90 225 100 231 110 229 120 221 130 208 140 196 150 178 160 170 86 180 53 190 39 200 29
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Channel Routing Example (Cont.)
Time Inflow C0I2 C1I1 C2Q1 Outflow (min) (cfs) 10 20 6 30 22 1 2 3 40 54 7 12 50 114 5 18 31 60 167 8 38 19 65 70 194 9 56 105 80 210 140 90 225 11 86 100 231 75 103 189 110 229 77 117 205 120 221 76 127 214 130 208 74 132 216 196 69 133 212 150 178 131 160 59 193 170 4 47 180 53 29 137 190 39 85 104 200 13 79 C0 = , C1 = , C2 =
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