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Flood Routing Example - Ref: Design of Small Dams (USBR) - 3rd Ed. - page 342

Original example has been done manually by trial & error method for each time step.

This SMath example does it prgrammatically using a "while" loop to iterate.

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cusec ft 3^s / :

Definitions

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acft acre ft * :

Inflow Hydrograph
From TABLE 9-1 & 
Fig 9.2) Inflow 040018002200034000460005470063300724008160091100115001240013400132 mat :

1. BASIC DATA

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Elevation H 300 300.3 301 302.1 303.8 305.3 306.2 306.6 306.7 91 mat ft * :

Storage ST 10501100121314491826219524182528255991 mat acft * :

Elevation & Storage

(Extracted from TABLE 9.1)

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From

Table 9.1

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From

Fig 9.2

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Extract first column

and assign "hr" unit

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T Inflow 1 col hr * :

Extract second column

and assign "cusec" unit

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Inf Inflow 2 col (cusec * :

Spill length

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L_spill 25 ft * :

73.66 ft *

Crest Elevation

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E_crest 300.0 ft * :

Bund Top Level

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BTL 310 ft * :

(Assumed)

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Water level at start

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E_start 300 ft * :

Full Supply Level

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FSL E_crest :

Spill discharge coefficient varies with head over spill crest

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Calculation of Cd, using "cases" function h Calc_Cd 0 h 0 ≤ 3.2 h 1 ≤ HH Cd h linterp h 5 ≤ 3.8 cases :

Cd 3.2 3.4 3.6 3.7 3.8 51 mat :

HH 1234551 mat :

From FIG 9.4)

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Ex. 0 Calc_Cd 0

Ex. 1 Calc_Cd 3.2

Ex. 2 Calc_Cd 3.4

Ex. 3 Calc_Cd 3.6

Ex. 4 Calc_Cd 3.7

Ex. 5 Calc_Cd 3.8

2. CALCULATIONS

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Max inflow

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I.max Inf max : cusec 6000

2.1 Spill discharge

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Overflow equation

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This is an Emperical formula, with fps units;
hence units must be balanced accordingly. h L_sp Q2 h ft / Calc_Cd L_sp ft / * h ft / (1.5^* cusec * :

Example 0.5 ft * L_spill Q2 cusec 28.3

2.2 Interpolating Functions

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x fit_ST H ft / ST acft / x linterp acft * :

300 fit_ST acft 1050

x FIT_S_E ST acft / H ft / x linterp ft * :

ST 1 el acft / FIT_S_E ft 300

Main Routing Program (SMath)

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PROGRAM 1 - Main Routing program I t e_start L_sp Rout n 1 el 1 : elv 1 el e_start : (WL at start ≡ elv 1 el E_crest ≤ (check WL at start ≡ h 1 el 0 : (no driving head if WL is below crest ≡ 11 line h 1 el elv 1 el E_crest - : (head above crest ≡ 11 line if st 1 el elv 1 el ft / fit_ST eval : (Storage at start ≡ I_avg 1 el 0 : (no avg inflow at start ≡ st_in_avg 1 el 0 : (no avg in_storage at start ≡ st_out_avg 1 el 0 : (no avg out_storage at start ≡ Δst 1 el 0 : (no change in storage st start ≡ st_total 1 el st 1 el Δst 1 el + : (tot. storage at start ≡ q_out 1 el h 1 el L_sp Q2 : q_out_avg 1 el 0 : counter 1 el 0 : 121 line j 2 I rows range n j el j : I_avg j el 0.5 I j el I j 1 - el + (* : st_in_avg j el I_avg j el t j el t j 1 - el - (* : st_total j el st_total j 1 - el st_in_avg j el + eval : ------------------- ------------------- elv j el st_total j el acft / FIT_S_E eval : elv j el E_crest ≤ st_out_avg j el 0 : h j el 0 : Δst j el st_in_avg j el : q_out j el 0 : q_out_avg j el 0 : counter j el 0 : 61 line h j el elv j el E_crest - : d1 E_crest : Δd 0.001 ft * : d 0.5 d1 * : counter j el 0 : d1 d - abs Δd ≥ d d1 : h j el d1 E_crest - eval : q_out j el h j el L_sp Q2 eval : q_out_avg j el 0.5 q_out j el q_out j 1 - el + (* : st_out_avg j el q_out_avg j el t j el t j 1 - el - (* : Δst j el st_in_avg j el st_out_avg j el - : st_total j el st_total j 1 - el Δst j el + eval : d1 st_total j el acft / FIT_S_E eval : elv j el d1 : counter j el counter j el 1 + : 101 line while 61 line if 81 line for A n t hr / I cusec / I_avg cusec / st_in_avg acft / augment eval : A A st_out_avg acft / Δst acft / st_total acft / h ft / augment eval : A A q_out_avg cusec / elv ft / q_out cusec / counter augment eval : 51 line :

Use routing program  
to get the results Ans1 Inf T E_start L_spill Rout :

Outflow Ans1 12 col cusec * :

Max_Outflow Outflow (max : cusec 1637.75

WL Ans1 11 col ft * :

Max_WL WL max : ft 306.67

Ans1 1040000001050003000021800600 49.59 0.53 49.06 1099.06 0.29 6.39 300.29 12.77 33220001400 115.7 3.77 111.93 1210.99 0.99 45.61 300.99 78.44 34340003000 247.93 13.84 234.09 1445.08 2.08 167.5 302.08 256.55 45460005000 413.22 38.44 374.78 1819.87 3.77 465.11 303.77 673.66 46547005350 442.15 75.29 366.86 2186.73 5.27 911 305.27 1148.33 47633004000 330.58 107.58 223 2409.73 6.17 1301.7 306.17 1455.06 48724002850 235.54 126.21 109.33 2519.06 6.57 1527.11 306.57 1599.16 49816002000 165.29 133.76 31.53 2550.59 6.67 1618.45 306.67 1637.75 410911001350 111.57 134.24 22.67 - 2527.92 6.6 1624.33 306.6 1610.92 41111500800 132.23 253.03 120.8 - 2407.12 6.16 1530.84 306.16 1450.75 51212400450 37.19 115.37 78.18 - 2328.94 5.84 1395.98 305.84 1341.2 41313400400 33.06 106.67 73.61 - 2255.33 5.54 1290.68 305.54 1240.16 41313 mat

Ans2 Inf T 300 ft * L_spill Rout :

E_start ft 300

Ans2 #

4 appVersion 0.99.7045.23606