Flood Routing
Ahmad Sana
Department of Civil and Architectural Engineering
Sultan Qaboos University
Sultanate of Oman
sana@squ.edu.om
http://ahmadsana.tripod.com/
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Hydrologic and
Hydraulic
Routing
Fig. 4-1
Reservoir Concepts
(a) Reservoir Storage
(b) Inflow and outflow
(c) Storage
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1
Example 4-1
Determine the average storage for each one-day period?
What is the maximum storage?
3
Time distribution of Storage
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2
Hydrologic
river routing
5
Muskingum
method
S = K [xI + (1 − x )Q ]
∆S
= I −Q
∆t
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3
Example 4-3:
Muskingum method
Given: Inflow, Initial
outflow, K and x.
Q2 = C0 I 2 + C1 I1 + C2Q1
− Kx + 0.5∆t
Determine: Outflow
D
kx + 0.5∆t
1. Calculate D, C0, C1 and
C1 =
C2.
D
K − Kx − 0.5∆t
2. Check if C0+C1+C2=1
C2 =
D
3. Calculate all Q values one
D = K − Kx + 0.5∆t
C0 =
by one.
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Example 4-4
Determination
of storage
coefficients
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4
9
Tutorial:
1. Problem 4.1
2. Problem 4.2
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5
Storage-Indication method
The continuity equation can be written as:
1
(I1 + I 2 ) − 1 (Q1 + Q2 ) = S 2 − S1
2
2
∆t
In general form it can be re-written as:
(I n + I n+1 ) + ⎛⎜ 2S n − Qn ⎞⎟ = ⎛⎜ 2S n+1 + Qn+1 ⎞⎟
⎝ ∆t
⎠ ⎝ ∆t
⎠
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Storage-Indication method
(I n + I n+1 ) + ⎛⎜ 2S n − Qn ⎞⎟ = ⎛⎜ 2S n+1 + Qn+1 ⎞⎟
⎝ ∆t
⎠ ⎝ ∆t
⎠
Given: Inflow, Initial Outflow, Storage-Discharge relationship
for reservoir
Determine: Outflow
1. Establish relationship between Q and 2S/Dt+Q using water
surface elevation in the reservoir, h.
2. Calculate left-hand-side for the above equation
3. Use the relationship of step 1 to determine Q at next time step
4. Repeat until you get Q for all time steps.
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6
Example 4-5:
Storage-Indication
method
Qorifice = Cd A0 2 gh
Qweir = (2 / 3)Ce 2 g L(h − h0 )1.5
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Example 4-5: Storage-Indication method
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7
Example 4-5: Storage-Indication method
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Tutorial:
1. Problem 4.4
2. Problem 4.21
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8
Hydraulic river routing
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Continuity Equation
∂A ∂Q
+
=q
∂t ∂x
Momentum Equation
∂v
∂v g ∂ ( yA) vq
+v +
+
= g (S 0 − S f )
∂t
x A ∂x
A
S f = S0 −
∂y v ∂v 1 ∂v
−
−
∂x g ∂x g ∂t
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