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HYDRAULICS OF CULVERTS Walter F. Silva, Ph.D., P.E. December 8 & 11, 2015 Walter F. Silva Araya, Ph.D., P.E.
HYDRAULICS OF CULVERTS
Walter F. Silva, Ph.D., P.E.
December 8 & 11, 2015
Walter F. Silva Araya, Ph.D., P.E.
UNIFORM, CRITICAL FLOW
and PIPE FLOW
Now you know…..
Walter F. Silva Araya, Ph.D., P.E.
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)
Walter F. Silva Araya, Ph.D., P.E.
EQUATIONS FOR WEIR AND ORIFICE
Walter F. Silva Araya, Ph.D., P.E.
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.
Walter F. Silva Araya, Ph.D., P.E.
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
Walter F. Silva Araya, Ph.D., P.E.
Inlet unsubmerged on steep slope with Weir Flow
Energy Equation:
Needs to compute critical depth in the conduit
Walter F. Silva Araya, Ph.D., P.E.
ycHW
𝐻𝑊 = 𝑦𝑐 + 1 + 𝐾𝑒𝑄2
2𝑔𝐴𝑐2
HW = Head above the invert of the culvert
Yc = critical depth
Ac = flow area corresponding to yc
Ke = entrance loss coefficient
d
Inlet control: Unsubmerged entrance Inlet unsubmerged on steep slope with Weir Flow
Rearranging the previous equation
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)
Walter F. Silva Araya, Ph.D., P.E.
𝑄 = 𝐶𝑑𝐴𝑐 2𝑔 𝐻𝑊 − 𝑦𝑐
HW = Head above the invert of the culvert
yc = critical depth
Ac = flow area corresponding to yc
Cd = Discharge coefficient
Inlet control: Submerged entrance Inlet Submerged on steep slope with Orifice flow
The orifice equation governs:
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)
Walter F. Silva Araya, Ph.D., P.E.
𝑄 = 𝐶𝑑𝐴0 2𝑔 𝐻𝑊
HW = Head above the invert of the culvert
Ao = Cross sectional area of the inlet
d= Discharge coefficient
Orifice Cd for culverts
Squared entrance
Walter F. Silva Araya, Ph.D., P.E.
0.4
0.42
0.44
0.46
0.48
0.5
0.52
0.54
0.56
0.58
0.6
1 1.5 2 2.5 3 3.5 4 4.5 5
HW
/d
Cd
Cd
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
Walter F. Silva Araya, Ph.D., P.E.
INLET TYPES
When tapered inlets are feasible, the improvement in
hydraulic performance can be significant in some cases.
Walter F. Silva Araya, Ph.D., P.E.
Walter F. Silva Araya, Ph.D., P.E.
Walter F. Silva Araya, Ph.D., P.E.
COMPARISON WITH DIFFERENT
IMPROVEMENTS
Walter F. Silva Araya, Ph.D., P.E.
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
Walter F. Silva Araya, Ph.D., P.E.
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
Walter F. Silva Araya, Ph.D., P.E.
Outlet Control with full flow conditions The pipe flow energy equation is:
Solving for the discharge:
Effective Head:
Head loss could be estimated using
Manning’s equation instead of Darcy-
Weisbach
Walter F. Silva Araya, Ph.D., P.E.
𝐻𝑊 = 𝑇𝑊 − 𝑆0𝐿 + 1 + 𝐾𝑒 + 𝑓𝐿
4𝑅
𝑄2
2𝑔𝐴2
𝑆0𝑇𝑊
𝑇𝑊
𝐸𝐺𝐿
𝑄 = 𝐴2𝑔 𝐻𝑊 − 𝑇𝑊 + 𝑆0𝐿
1 + 𝐾𝑒 + 𝑓𝐿4𝑅
𝐻𝑒𝑓𝑓 = 𝐻𝑊 − 𝑇𝑊 + 𝑆0𝐿
𝑓𝐿
4𝑅=2𝑔𝑛2𝐿
𝐾𝑛2𝑅4/3
Kn = 1 for SI and 1.49 for ES FHWA developed Outlet control nomographs
based on Effective Head
ROADWAY OVERTOPPINGThe flow will be similar to flow over a broad crested weir.
Walter F. Silva Araya, Ph.D., P.E.
An iterative procedure must be used to divide flow between
the culvert and the embankment flow
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 Walter F. Silva Araya, Ph.D., P.E.
PERFORMANCE CURVES
One more thing you need to know…..
Walter F. Silva Araya, Ph.D., P.E.
PERFORMANCE CURVES1. 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 vice-versa 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.
Walter F. Silva Araya, Ph.D., P.E.
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.
Walter F. Silva Araya, Ph.D., P.E.
PERFORMANCE CURVE FOR ALL CONDITIONS
Walter F. Silva Araya, Ph.D., P.E.
DESIGN USING
NOMOGRAPHS
WORKSHOP 2
Walter F. Silva Araya, Ph.D., P.E.
