bridges and culverts: water velocity and...

FRST 557

Lecture 7c

Bridges and Culverts: Water Velocity and Discharge

Lesson Background and Overview:

The previous two lessons presented methods for estimating water volume flow at a particular site and introduced different types of structures that allow water to pass under a road. This final lesson on water management looks at designing the structure for the volume and velocity of the anticipated water flow.

This cedar log culvert was constructed for a railroad logging operation in the late 1920s and is still functioning over 75 years later.

Lesson Objective:

On completion of this lesson and the associated assignment, you will have a general idea of how bridge openings are determined and you will be able to calculate velocity and volume for water in culverts.

Lesson References:

BC Ministry of Forests. September 1995. Forest Road Engineering Guidebook. Forest Practices Code of British Columbia. “Stream Culvert Discharge Design” (This is no longer in print, but a copy is available with the course notes under FOPR 262 / Supplemental / FRE Guide Stream Discharge) BC Ministry of Forests. June 2002. Forest Road Engineering Guidebook. Forest Practices Code of British Columbia. Chapter 4. Road Drainage Construction BC Ministry of Forests. 1998. Stream Crossing Guidebook for Fish Streams. Forest Practices Code of British Columbia. pp. 10-15 (Sections 3.1 and 3.2), pp. 29-33 (Section 5), pp. 66-79 (Appendix 4.1 - 4.5 and Appendix 6) (This is no longer in print, but this information is available with the course notes under FOPR 262 / Supplemental / SC Guide Fish) BC Ministry of Forests. March 2002. Fish Stream Crossing Guidebook. Forest Practices Code of British Columbia. American Iron and Steel Institute. 1984. Handbook of Steel Drainage & Highway Construction Products - Canadian Edition Nagy, M.M. et al. 1980. Log Bridge Construction Handbook. Forest Engineering Research Institute of Canada, Vancouver

FRST 557 - Lecture 7c Bridges and Culverts: Water Velocity & Discharge

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Designing Bridges and Culverts

Bridges

The site assessment for bridge crossings considers the cross sectional area of flowing water at the design event at the site of the bridge. Allowance is also considered in the bridge design for debris floating (or tumbling) downstream during storm events, Ideally, allowance is made for the flow to pass below the bridge unrestricted. That is, the channel is undisturbed by the bridge. If it is not possible for the channel to be bridged without some restriction (e.g. an intermediate piling support) then allowance must be made for additional area to compensate for the area lost to the obstruction. At any point in time, flow volume will be constant whether or not a restriction is present (Q = VA). A restriction may alter the values of velocity (V) and area (A) but the product (Q) will be the same. An exception to this is where the restriction becomes sufficient to actually partially dam the flow and cause water levels to rise. The economic and environmental risks of under designing a bridge make it prudent to seek appropriate professional assistance early in the planning process

Culverts

Culverts, because of the relatively small water flow, require shorter spans and are most often constructed with either pre-designed and purchased structures (e.g. metal or “plastic” pipes) or logs meeting appropriate loading specifications. Culverts do not normally require professional design unless extraordinary risks exist. However, diligence at making adequate provision for water passage is required. It is usually expected that provision will be quite conservative.

Culvert design for opening area

The fastest and most simple method of designing culverts for capacity is to estimate the cross section area of the planned storm event. As stated in the last lesson, the design standard in British Columbia for a major culvert is the peak flow of the 100 year event (Q100). The basis for this calculation is the measurement of the “bank-full event” which occurs approximately every 2.3 years on the average. The volume and cross-sectional area of this event are represented as Q2 and A2. Based on empirical data, the 100 year event (Q100) is considered to be 3 times Q2. While this ratio is not expected to be representative of all situations, it is considered to be adequate for situations requiring culverts under 2000 mm diameter and streams with volume flows of under 6 m

3/sec. Since Q100 = 3Q2 and since area is directly proportional to the volume, A100 = 3A2

Although A2 can be determined by more detailed and precise means, the following method is quite adequate for many situations.


3

W1

W2

D

Determining Culvert Size: Q100 Area Method

1. The stream is measured for width at the bank tops (W1) and the stream bed (W2). 2. The average depth (D) of the bank full event may be based on the average of

several readings. 3. The cross sectional area is calculated using:

A2 = [(W1 + W2)/2]D

4. The culvert opening is calculated using A100 = 3A2

The culvert may be any shape, provided that this opening size is maintained. Example:

W1 = 2.25 m W2 = 1.75 m D = 0.5 m A2 = [(2.25 +1.75)/2]0.05 = 1.0 m

2

A100 = 3(1.0) = 3.0 m

2

This area could be met with a rectangular culvert of 3m width and 1 m depth or a round pipe of

mmm

AD 1954954.1

0.344

Since culvert pipes come in standard sizes of 200 mm increments, a 2000mm pipe would be chosen.


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Simple Log Culvert

(Source: BC Ministry of Forests. September 1995. Forest Road Engineering Guidebook. Forest Practices Code of British Columbia. Figure 23)

Log Culvert Stringer Table (diameter at mid-span in meters)

(Source: BC Ministry of Forests. September 1995. Forest Road Engineering Guidebook. Forest Practices Code of British Columbia. Table 12.)


5

Culvert design using a Nomograph

A nomograph is a graphic solution of an equation. In this case, we will use a nomograph for a corrugated metal culvert were the variables are:

Type of culvert entrance (inlet control)

Depth of water at entrance

Culvert diameter

Water volume discharge Knowledge of three of the variables provides the unknown. The nomograph assumes a very shallow gradient and that there are no restrictions at the outflow end (including a submerged outflow).

Example of

Nomograph Use

Culvert has a diameter of 900 mm. It

is installed with a type 3 entrance

and the water at the entrance

(headwater depth) is 1980 mm

(= 2.2 times the pipe diameter).

1. Locate the Headwater depth ratio

on the scale for the type 3 entrance.

2. Project a horizomtal line across to

the inner ( type 1) scale.

3. Project a line to the culvert

diameter (900 mm).

4. Read off the volume discharge

(Q = 1.8 m3 / second)

The nomograph illustrated here is one of many available for many different shapes and sizes of culverts. Because nomographs are based on thorough empirical data, they do provide an excellent means of selecting suitable structures for known flow volumes.


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Example: Returning to the previous example:

2.25 m

1.75 m

0.5m0.56 m0.56 m

W1 = 2.25 m W2 = 1.75 m

D = 0.5 m

A2 = [(2.25 +1.75)/2]0.05 = 1.0 m2

In this case, we want to work with volumes rather than just areas, so we need two other variables to calculate the stream flow with Manning’s equation. Let’s assume:

Stream gradient or slope (S) is 2% = 0.02

Manning’s coefficient is 0.076 The wetted perimeter is the sum of the stream bed (W2) plus the two banks:

Pw = 1.75 + 0.56 + 0.56 = 2.87 The hydraulic radius R = A/Pw = 1.0/2.87 = 0.35

93.0

076.0

02.035.02/13/22/13/2

2 n

SRV m / second

Q2 = V2A2 = (0.93)(1.0) = 0.93 m

3 / second

Q100 = 3Q2 = 3(0.93) = 2.79 m3 / second

Going to the nomograph and assuming a type 3 entrance and a 90% water depth at the culvert entrance, a 1500 mm culvert is indicated which is sized up to the nearest 200 mm or 1600 mm diameter.


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Culvert design using Manning’s

CAUTION: The previous examples of culvert size selection should direct you to a reasonably safe conclusion. This example will produce figures that may not adequately consider all of the restrictive dynamics of a culvert flowing at the higher range of its capacity. Because of this, caution should be exercised in using this as a method of determining a culvert size for the purpose of handling a particular water volume. We will use this method to design culverts that will provide suitable velocities for fish passage. As with any watercourse, a pipe of any type will have physical attributes that affect the rate of water flow over its surface. Pipe diameter affects the ratio of the cross sectional area to the wetted perimeter (R = A / Pw). Surface roughness and irregularities affect the “friction” and turbulence of the flow, which is expressed as a Manning’s coefficient (n). The corrugation of metal culvert pipes is a major part of the coefficient. It is measured in terms of pitch x depth and by the direction of the corrugation.

Pitch (P)

Depth (D)

Shape of corrugated metal for a culvert pipe.

Specifications will include the metal thickness

(“gauge”) and P x D (e.g. 76 mm x 25 mm)

Some corrugated metal pipes (CMP) are filled, or partly filled with asphalt (“paved”) to reduce the coefficient. The following table provides Manning coefficients for several different types and sizes of CMP.

Helical Corrugation Annular Corrugation


8

68x13m m 1400

A ll &

D iam e te rs La rge r

Unpaved 0 .024 0 .012 0 .011 0 .013 0 .014 0 .015 0 .018 0 .018 0 .020 0 .021

25% P aved 0 .021 0 .014 0 .017 0 .020 0 .019

F ully P aved 0 .012 0 .012 0 .012 0 .012 0 .012

A nnula r 2200 &

76x25m m Large r

Unpaved 0 .027 0 .023 0 .023 0 .024 0 .025 0 .026 0 .027

25% P aved 0 .023 0 .020 0 .020 0 .021 0 .022 0 .022 0 .023

F ully P aved 0 .012 0 .012 0 .012 0 .012 0 .012 0 .012 0 .012

A nnula r 2000 &

125x26m m Large r

Unpaved 0 .025 0 .022 0 .023 0 .024 0 .025

25% P aved 0 .022 0 .019 0 .020 0 .021 0 .022

F ully P aved 0 .012 0 .012 0 .012 0 .012 0 .012

900 1200300 400 500 600

He lica l

C o rruga tions

A nnula r

V alu es o f C o effic ien t o f Ro u g h n ess (n )

fo r S tan d ard C o rru g ated S tee l P ip e

(M an n in g 's F o rm u la )

38x65m m 68x13m m

200 250

He lica l - 76x25m m

He lica l - 125x26m m

1400 1600 1800

1200 1400 1800 20001600

Taking the results of the previous example, let’s assume that the 1600 mm culvert is a Helical 76 mm x 25 mm unpaved pipe with n = 0.024 (from the table). Installed at the creek gradient, the slope S = 2% or 0.02 Now using the Manning equation, we will determine the rate of flow where, like the last example, the water level is to 90% of the culvert diameter.

/2

D

d

d-r r

r

360° -

W

d-r W/2

/2

Where pipe is more than ½ full d > r

D = 1600mm = 1.6 m r = D/2 = 0.8 m d = 90% of D = 0.9(1.6) = 1.44 m d-r = 0.64 m


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Manning’s equation for velocity is:

n

SRV

2132

where:

V = the calculated velocity of flow in m / second R = the hydraulic radius ( = A / Pw )

A = the cross sectional area of the stream (m2) (water in culvert)

Pw = wetted perimeter (m)

S = the slope of the channel segment (m / m) n = coefficient of roughness (see tables)

The most challenging part of this assignment is to determine the cross sectional area and wetted perimeter to calculate the hydraulic radius. This requires us to identify some basic shapes in the diagram for which we can calculate area (and perimeters), and then add or subtract the identified areas to get the numerical value for our subject shape. One option in this case is to get the area and the Pw of:

And then add the area of the missing triangle Going back to the diagram of the whole culvert cross section:

Find :

7.73

800.08.0

64.0

2cos

r

rd

The upper surface of the water: mrW 96.02

sin2

This additional information is all that is needed to calculate the wetted perimeter and area:

mDPw 00.4360

360

22 91.131.060.12

1360

360mrdWrA

Next the hydraulic radius is:

mP

AR

w

48.000.4

91.1


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The velocity using Manning’s is:

sec/60.3

024.0

02.048.05.67.2132

mn

SRV

Finally, the volume:

sec/88.660.391.1 3mAVQ

If we compare the Q of this calculation with the Q100 (2.79 m

3 / second) used when the 1600 mm

culvert was selected from the nomograph, we see a significantly higher figure. This may be confusing at first, but recall that this latest calculation is for just one point in the culvert, and it does not consider all of the dynamics taking place in the entire culvert and its two ends. Also, this calculation used a 2% slope for the culvert, where the nomograph did not consider slope differences. If a lesser slope is used, the velocity and volume is significantly reduced. Retaining the 90% headwater depth but changing the culvert slope, the Manning equation will produce the following:

Slope V (m/sec) Q (m3/sec)

2% 3.60 6.88

1% 2.55 4.31

0.1% 0.81 1.54

Culvert half full or less

It is important to note that the calculations change if the water level is at ½ or less than ½. For a pipe running half full:

DP

and

rA

w

5.0

5.0 2


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For a pipe less than ½ full, examine the differences in the geometry:

/2

D

d

r-d r

r

360° -

W

r-d W/2

/2

Where pipe is less than ½ full d < r

In this case to get the area and the Pw first use:

And then subtract the area of the surplus triangle

(Note that the height of the triangle changes from: d - r (if d > r)

to r - d (in this case where d < r)

Culvert variables and their effect

Looking at Manning’s equation again, the following relationships between each variable and the resultant velocity (and therefore volume) can be seen for a given culvert diameter.

n

SRV

2132

As the water depth decreases, velocity decreases (because the value of R goes down)

As slope (S) decreases, velocity decreases

Anything that increases the coefficient of roughness (n) will decrease the velocity.


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Fish Passage

When crossing fish bearing watercourses, the ideal is to leave the streambed entirely intact by constructing a bridge or an open bottom culvert that spans the entire channel and leaves the bed in a natural condition. Assuming sufficient depth of water, pipe culverts can affect fish passage by either creating a physical barrier (e.g. an elevated outfall too high for the fish to reach) or by accelerating the velocity of water flow to beyond the swimming capabilities of the fish. Refer to the “Stream Crossing Guidebook for Fish Streams (1998)” and “Fish Stream Crossing Guidebook (2002)” for a discussion on fish passage parameters. Specifically, look at the tables that provide information on the maximum capabilities of various fish to travel upstream. Critical water levels for the fish passage are calculated using a “channel flow maintenance level” which is illustrated below. The velocity and volume of water flow at this point are called “high passage” and are labeled Vhp and Qhp.

Source: FPC: Stream Crossing for Fish Streams

Guidebook

Calculations of Vhp and Qhp are performed as previously described, except for the reduced area and wetted perimeter. The culvert must still be designed for Q100, but that design is then checked for water flow Qhp. If Vhp exceeds the ability of the fish, the culvert variables must be adjusted to slow down the velocity.


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Velocity can be slowed by:

Increasing the culvert size, which will reduce the depth of flow and the hydraulic radius

Reducing the slope

Increasing “n” by sinking the culvert into the streambed and filling the culvert bottom with materials (e.g. rock, boulders) similar to the natural streambed. This is called “embedment”. “Baffles” may also be installed in the pipe.

Whenever the culvert velocity is reduced from the Q100 design, the culvert must be rechecked to ensure that it will still carry the volume at the 100-year event. Baffles or embedment effectively reduce the area available for water flow and must be considered in the new calculations. It may take several attempts to match an appropriate culvert size and installation for both fish passage and the 100-year event.

A final remark

Stream flow calculations and culvert design are obviously not an exact science. The ability to assess a site for appropriate evidence and to anticipate factors that will affect culvert performance require skilled application of the knowledge of the planner.


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