1d steady state hydraulic modelling bratton stream case study
TRANSCRIPT
1D Steady State
Hydraulic Modelling
Bratton Stream Case Study
How does a steady state computer model work?
1. Topographic Survey
X-section 4 geometry
12
3
45
6
7
Downstream
Upstream
Chainage ∆x
How does a steady state computer model work?
BUT, what will the water depth be at each cross-section?
2. Boundary Conditions
12
3
45
6
7
Downstream – WATER DEPTH, y1
Upstream – DISCHARGE, Q
Chainage ∆x
e.g. 1 in 100 yr RP (constant Q)
e.g. flood hydrograph ( Q v. time)
e.g. flow over weir; gauging station
We need to calculate flow depth at each cross-section
How does a steady state computer model work?
3. Standard Step Method
12
3
45
6
7
Downstream – WATER DEPTH, y1
Upstream – DISCHARGE, Q
Chainage ∆x
So…given y at (1) how does the model calculate y at (2)?
y2
2(U22 / 2g)
ΣHe
Chainage, ∆x
X-SECTION
(1)
z2
1(U12 / 2g)
y1
z1
X-SECTION
(2)
Velocity Head
Energy gradient Sf
Hydraulic gradient Sws
Head Loss
AB
SO
LUTE H
EA
D i.e
. B
ER
NO
ULL
I’S
y2
2(U22 / 2g)
ΣHe
z2
1(U12 / 2g)
y1
z1
Sf
Sws
z2 + y2 + α2 (U22/2g) == ΣHe + z1 + y1 + α1 (U1
2/2g)
Chainage, ∆x
y1 is known Q is known from river gauge
Geometry is known
z2 + y2 + α2 (U22/2g) == ΣHe + z1 + y1 + α1 (U1
2/2g)
U = Q / A
Energy line E1 = z1 + y1 + α1(U12/2g)
α = 1.15 to 1.50
y1 is known Q is known from river gauge
Geometry is known
z2 + y2 + α2 (U22/2g) == ΣHe + z1 + y1 + α1 (U1
2/2g)
U = Q / A
Energy line E1 = z1 + y1 + α1(U12/2g)
α = 1.15 to 1.50
Geometry is knownChainage (∆x) is known
But we don’t know ΣHe, U2 or y2
z2 + y2 + α2 (U22/2g) == ΣHe + z1 + y1 + α1 (U1
2/2g)
Rearrange to solve for y2
y2 == ΣHe + z1 - z2 + y1 + α1 (U12/2g) - α2 (U2
2/2g)
ΣHe = Sf dx
y2 == ΣHe + z1 - z2 + y1 + α1 (U12/2g) - α2 (U2
2/2g)
y2 == ΣHe + z1 - z2 + y1 + α1 (U12/2g) - α2 (U2
2/2g)
ITERATE for y2 & U2
e.g. guess y2
Use known geometry and Q = UA to solve for U2
Given U22/2g and Sf, … does the
equation work? Repeat iteration.
y2 == ΣHe + z1 - z2 + y1 + α1 (U12/2g) - α2 (U2
2/2g)
ITERATE for y2 & U2
e.g. guess y2
Use known geometry and Q = UA to solve for U2
Given U22/2g and Sf, … does the
equation work? Repeat iteration.
Bratton Stream
Case Study
ObjectiveTo accurately model stage – Q curve at site of proposed
flow gaugeGrass floodplain
Bund + path
Culvert under road
Weir (700mm drop)
Cobble bed
400mm walled banks
Topographic Survey
10m chainage6 X-sections1 weir2 bridges1 gauge
Bridge
Weir
X-sections
Bench mark
0.07
3
0.05
60.06
2
0.03
30.04
3
0.01
2
0.01
40.
002
0.00
0
0.001
0.013
0.020
0.02
50.
019
0.09
10.
083
HEC-RAS set-up
Your model has already been set-up to include:
Geometry & structures Downstream boundary
- normal depth Upstream boundary
- critical depth Manning’s ‘n’
0.02-0.04 (channel)
0.03-0.07 (floodplain)
HEC-RAS set-upBratton is an Un-gauged catchment, hence Q for flood RP need estimating from the Flood Estimation Handbook (FEH).
Used 3 donor catchments of similar character to give Qmed = 1.42cumecs
Your task…
Investigate the effect of the 1in50, 100 & 200yr RP on stage at the proposed gauging station (node ref. 0.062)
Investigate model sensitivity to flow Q by taking into account +20% change in peak Q over the next 50yrs due to climate change