HYDRAULICS OF CULVERTS - T2 Centerprltap.org/eng/wp-content/uploads/2015/12/Culverts...HDS-5 culvert design methods are based on design charts and nomographs. These charts and nomographs

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.