HYDRAULICS OF CULVERTS

Transcription

1 HYDRAULICS OF CULVERTS Walter F. Silva, Ph.D., P.E. December 8 & 11, 2015

2 Now you know.. UNIFORM, CRITICAL FLOW and PIPE FLOW

3 Classification of Culvert Flow USGS classifies culvert flow into six types, depending on the headwater and tailwater levels and whether the slope is mild or steep (Bodhaine, 1986)

4 EQUATIONS FOR WEIR AND ORIFICE

5 Submergence Criteria INLET SUBMERSION OCCURS WHEN THE RATIO OF THE INLET HEAD TO THE CULVERT HEIGHT (HW/d) IS IN THE RANGE OF 1.2 TO 1.5.

6 Inlet Control In steep slopes and low headwater and tailwater levels the flow passes through the critical depth at the inlet and downstream is supercritical S2 curve approaching normal depth If the outlet is submerged there will be a hydraulic jump inside the culvert Type 1

7 Inlet unsubmerged on steep slope with Weir Flow Energy Equation: Q 2 HW = y c K e 2 2gA c HW = Head above the invert of the culvert Yc = critical depth Ac = flow area corresponding to yc Ke = entrance loss coefficient Needs to compute critical depth in the conduit HW y c d

8 Inlet control: Unsubmerged entrance Inlet unsubmerged on steep slope with Weir Flow Rearranging the previous equation Q = C d A c 2g HW y c HW = Head above the invert of the culvert y c = critical depth Ac = flow area corresponding to yc Cd = Discharge coefficient Circular culvert with squared edge Cd = 0.93 if HW/d < 0.4 Circular culvert with squared edge Cd = 0.80 if HW/d = 1.5 Cd can be corrected for bevels and rounding of the entrance Box culverts flush in vertical headwall Cd = 0.95 (USGS type 1 flow)

9 Inlet control: Submerged entrance Inlet Submerged on steep slope with Orifice flow The orifice equation governs: Q = C d A 0 2g HW HW = Head above the invert of the culvert Ao = Cross sectional area of the inlet d= Discharge coefficient The orifice coefficient varies according to the degree of rounding, the bevel height and the degree of submergence (HW/d) The purpose of the bevel is to reduce the flow contraction at the inlet (increase the Cd)

10 HW/d Orifice Cd for culverts Squared entrance Cd Cd

11 OTHER IMPROVEMENTS FOR INLET CONTROL The FHWA did extensive experimental work on culverts Improvements for inlet control includes: Bevels Mitered entrances Wingwalls Side tapered inlets Depressions Their purpose is to increase the flow passing through the culvert by improving the entrance conditions

12 INLET TYPES When tapered inlets are feasible, the improvement in hydraulic performance can be significant in some cases.

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15 COMPARISON WITH DIFFERENT IMPROVEMENTS

16 NOMOGRAMS The FHWA developed inlet control nomographs considering improvements by wingwalls and side tapered inlets and depressions Their purpose is facilitate hand-made design calculations Good for first trial and quick estimates

17 Outlet Control Type 4 (Figure D) is full pipe flow conditions under pressure In Type 6 (Figure B) outlet is unsubmerged but culvert flows full Critical depth could occur at the outlet in Figure B Type 2 and 3 are open channel flow, subcritical flow on mild slope (Figs. A and C) Cases B and D are treated as full flow

18 Outlet Control with full flow conditions The pipe flow energy equation is: HW = TW S 0 L K e + f L 4R Q 2 2gA 2 Solving for the discharge: EGL Q = A 2g HW TW + S 0L 1 + K e + f L 4R TW TW Effective Head: H eff = HW TW + S 0 L S 0 Head loss could be estimated using Manning s equation instead of Darcy- Weisbach f L 4R = 2gn2 L K n 2 R 4/3 K n = 1 for SI and 1.49 for ES FHWA developed Outlet control nomographs based on Effective Head

19 ROADWAY OVERTOPPING The flow will be similar to flow over a broad crested weir. An iterative procedure must be used to divide flow between the culvert and the embankment flow

20 CULVERT DESIGN IS A TRIAL AND ERROR PROCEDURE BOTH INLET AND OUTLET CONTROL MUST BE CALCULATED COMPARE WITH ALLOWABLE HEADWATER ELEVATION CHOOSE THE HIGHER HEAD FOR A GIVEN DISCHARGE DO A PERFORMANCE ANALYSIS TO DETERMINE OPERATION OF THE CULVERT UNDER DIFFERENT CONDITIONS UNSUBMERGED INLET IN CULVERTS OPERATES AS WEIR OR ORIFICE FLOW PRESSURIZED FLOW MUST BE ANALYZED BY EFFECTIVE HEAD: DIFFERENCE BETWEEN TOTAL HEAD AT THE HEADWATER AND THE TAILWATER

21 One more thing you need to know.. PERFORMANCE CURVES

22 PERFORMANCE CURVES 1. Plot of headwater depth or elevation versus flow rate. 2. Useful in evaluating the hydraulic capacity of a culvert for various headwaters. 3. Displays the consequences of higher flow rates at the site. 4. Both inlet and outlet control curves must be plotted. 5. Dominant control at a given headwater is hard to predict 6. Control may shift from the inlet to the outlet or viceversa over a range of flow rates. 7. Using the concept of minimum performance the figure shows that, at the allowable headwater the culvert operates under inlet control.

23 CULVERT HYDRAULICS IN HDS-5: MINIMUM PERFORMANCE and ACCURACY Minimum performance means that while the culvert may operate more efficiently at times (more flow for a given headwater level), it will never operate at a lower level of performance than calculated HDS-5 culvert design methods are based on design charts and nomographs. These charts and nomographs are based on data from hydraulic tests and on theoretical calculations. There is scatter in the test data and the selection of a best fit design equation. The correlation between the design equations and the design nomographs is not exact. Reproduction of the design charts introduces additional error. The results of the procedure are accurate to within plus or minus ten percent, in terms of headwater elevation.

24 PERFORMANCE CURVE FOR ALL CONDITIONS

25 WORKSHOP 2 DESIGN USING NOMOGRAPHS