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