Problem 10-1

With K = 2 h, and Δt = 1 h, the routing coefficients (eqs. 8-16 to 8-18) are: C₀ = 1/5; C₁ = 1/5; and C₂ = 3/5.
The routing computations are shown in the following table.

The calculated peak outflow is 195.26 m³/s, and it occurs at 8 h.  ANSWER.

Problem 10-2

With K = 2 h: S = 2 x (O). With Δt = 1 h, the storage-indication-outflow relation O = [(2 x S / Δt) + O] is: O = (1 / 5) x [(2 x S / Δt) + O].
The calculations are shown in the following table.

The calculated peak outflow is 195.26 m³/s, and it occurs at 8 h.  ANSWER.

Problem 10-3

Using program EH800 with the given reservoir data and design flood conditions, the peak outflow is: Q_p = 164.585 m³/s.
The maximum water surface elevation corresponding to this peak outflow is: 123.07 m. Since the dam crest elevation is at 125 m, the actual freeboard is: FB = 125.0 - 123.07 = 1.93 m.   ANSWER.
The computer run for this problem is provided below.

THANK YOU FOR RUNNING EH800.
THIS PROGRAM ROUTES A FLOOD WAVE THROUGH A NATURAL RESERVOIR
ASSUMING THE INITIAL POOL LEVEL AT OR ABOVE SPILLWAY CREST.
ARE YOU USING SI UNITS (Y/N)?: y
IN SI UNITS USE M, M3/S, AND HM3.
ANSWERS WILL BE GIVEN IN M AND M3/S.

ENTER WIDTH OF THE EMERGENCY SPILLWAY (M OR FT): 18
ENTER COEFFICIENT OF THE SPILLWAY RATING: 1.7
ENTER EXPONENT OF THE SPILLWAY RATING: 1.5
ENTER SPILLWAY CREST ELEVATION (M OR FT): 120
ENTER DAM CREST ELEVATION (M OR FT): 125
ENTER INITIAL RESERVOIR LEVEL (M OR FT): 120
ENTER NUMBER OF ELEVATION-STORAGE DATA PAIRS: 6
ARE YOU READING ELEVATION-STORAGE PAIRS INTERACTIVELY (Y/N)?: y
ENTER 6 ELEVATION-STORAGE DATA PAIRS (M OR FT, AND HM3 OR AC-FT): 120 3.00
121 3.05
122 3.15
123 3.35
124 3.75
125 4.25
ENTER TIME INTERVAL (H): 1
ENTER NUMBER OF INFLOW VALUES: 23
PLEASE NOTE THAT THE FIRST INFLOW VALUE SHOULD CORRESPOND
TO THE END OF THE FIRST TIME STEP.
ARE YOU READING INFLOW VALUES INTERACTIVELY (Y/N)?: y
15 30 45 70 100 125 150 175 165 140 125 100 80 60 50 33 25 14 9 7 5 1 0
DO YOU WANT YOUR OUTPUT TO THE SCREEN (Y/N)?: y

MAXIMUM POOL ELEVATION= 123.070 M.
THANK YOU FOR RUNNING EH800. PLEASE CALL AGAIN.

Problem 10-4

With the given reservoir and design flood conditions, the objective is to determine the emergency spillway width (rectangular cross section) that produces a maximum water surface elevation of 481.0 m, i.e., the diference between dam crest elevation (483.0 m) and design freeboard (2.0 m). The calculation proceeds by trial and error, using program EH800. The trials are summarized in the following table.

Emergency spillway width			Maximum water surface elevation
(m)			(m)
8			481.624
9			481.315
10			481.089
10.20			481.049
10.40			481.010

THANK YOU FOR RUNNING EH800.
THIS PROGRAM ROUTES A FLOOD WAVE THROUGH A NATURAL RESERVOIR
ASSUMING THE INITIAL POOL LEVEL AT OR ABOVE SPILLWAY CREST.
ARE YOU USING SI UNITS (Y/N)?: y
IN SI UNITS USE M, M3/S, AND HM3.
ANSWERS WILL BE GIVEN IN M AND M3/S.

ENTER WIDTH OF THE EMERGENCY SPILLWAY (M OR FT): 10.4
ENTER COEFFICIENT OF THE SPILLWAY RATING: 1.7
ENTER EXPONENT OF THE SPILLWAY RATING: 1.5
ENTER SPILLWAY CREST ELEVATION (M OR FT): 475
ENTER DAM CREST ELEVATION (M OR FT): 483
ENTER INITIAL RESERVOIR LEVEL (M OR FT): 475
ENTER NUMBER OF ELEVATION-STORAGE DATA PAIRS: 5
ARE YOU READING ELEVATION-STORAGE PAIRS INTERACTIVELY (Y/N)?: y
ENTER 5 ELEVATION-STORAGE DATA PAIRS (M OR FT, AND HM3 OR AC-FT): 475 5.1
477 5.3
479 5.6
481 6.4
483 7.6
ENTER TIME INTERVAL (H): 1
ENTER NUMBER OF INFLOW VALUES: 24
PLEASE NOTE THAT THE FIRST INFLOW VALUE SHOULD CORRESPOND
TO THE END OF THE FIRST TIME STEP.
ARE YOU READING INFLOW VALUES INTERACTIVELY (Y/N)?: y
10 30 50 90 150 250 350 280 210 190 170 130 100 90 75 50 40 30 15 10 5 2 1 0
DO YOU WANT YOUR OUTPUT TO THE SCREEN (Y/N)?: y

MAXIMUM POOL ELEVATION= 481.01 M.
THANK YOU FOR RUNNING EH800. PLEASE CALL AGAIN .