1. 1D Steady State Hydraulic Modelling Bratton Stream Case Study

2. How does a steady state computer model work? 1. Topographic Survey X-section 4 geometry 1 2 3 4 5 6 7 Downstream Upstream Chainage ∆x

3. How does a steady state computer model work? BUT, what will the water depth be at each cross-section? 2. Boundary Conditions 1 2 3 4 5 6 7 Downstream – WATER DEPTH, y 1 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

4. We need to calculate flow depth at each cross-section How does a steady state computer model work? 3. Standard Step Method 1 2 3 4 5 6 7 Downstream – WATER DEPTH, y 1 Upstream – DISCHARGE, Q Chainage ∆x So…given y at (1) how does the model calculate y at (2)?

5. y2y2  2 (U 2 2 / 2g) ΣHeΣHe Chainage, ∆x X-SECTION (1) z2z2  1 (U 1 2 / 2g) y1y1 z1z1 X-SECTION (2) Velocity Head Energy gradient S f Hydraulic gradient S ws Head Loss ABSOLUTE HEAD i.e. BERNOULLI’S

6. y2y2  2 (U 2 2 / 2g) ΣHeΣHe z2z2  1 (U 1 2 / 2g) y1y1 z1z1 SfSf S ws = z 2 + y 2 + α 2 (U 2 2 /2g) = ΣH e + z 1 + y 1 + α 1 (U 1 2 /2g) Chainage, ∆x

7. y 1 is known Q is known from river gauge Geometry is known = z 2 + y 2 + α 2 (U 2 2 /2g) = ΣH e + z 1 + y 1 + α 1 (U 1 2 /2g) U = Q / A Energy line E 1 = z 1 + y 1 + α 1 (U 1 2 /2g) α = 1.15 to 1.50

8. y 1 is known Q is known from river gauge Geometry is known = z 2 + y 2 + α 2 (U 2 2 /2g) = ΣH e + z 1 + y 1 + α 1 (U 1 2 /2g) U = Q / A Energy line E 1 = z 1 + y 1 + α 1 (U 1 2 /2g) α = 1.15 to 1.50 Geometry is known Chainage (∆x) is known But we don’t know Σ H e, U 2 or y 2

9. = z 2 + y 2 + α 2 (U 2 2 /2g) = ΣH e + z 1 + y 1 + α 1 (U 1 2 /2g) Rearrange to solve for y 2 = y 2 = ΣH e + z 1 - z 2 + y 1 + α 1 (U 1 2 /2g) - α 2 (U 2 2 /2g) ΣH e = S f dx = y 2 = ΣH e + z 1 - z 2 + y 1 + α 1 (U 1 2 /2g) - α 2 (U 2 2 /2g)

10. ITERATE for y 2 & U 2 e.g. guess y 2 Use known geometry and Q = UA to solve for U 2 Given U 2 2 /2g and S f, … does the equation work? Repeat iteration.

11. = y 2 = ΣH e + z 1 - z 2 + y 1 + α 1 (U 1 2 /2g) - α 2 (U 2 2 /2g) ITERATE for y 2 & U 2 e.g. guess y 2 Use known geometry and Q = UA to solve for U 2 Given U 2 2 /2g and S f, … does the equation work? Repeat iteration.

12. Bratton Stream Case Study

13. Objective To accurately model stage – Q curve at site of proposed flow gauge Grass floodplain Bund + path Culvert under road Weir (700mm drop) Cobble bed 400mm walled banks

14. Topographic Survey 10m chainage 6 X-sections 1 weir 2 bridges 1 gauge Bridge Weir X-sections Bench mark 0.073 0.056 0.062 0.033 0.043 0.0120.0140.002 0.000 0.001 0.013 0.020 0.025 0.019 0.091 0.083

15. 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)

16. HEC-RAS set-up Bratton 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 Q med = 1.42cumecs

17. 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