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FHWA > Engineering > Hydraulics > HEC 14 > Chapter 3 
Hydraulic Design of Energy Dissipators for Culverts and Channels

Culvert Diameter Change (SI) mm  914 to 1219  1219 to 1524  1524 to 1829 

Culvert Diameter Change (CU) ft  3 to 4  4 to 5  5 to 6 
Percent Reductin in Outlet Velocity (V=Q/A)  44%  35%  31% 
For high tailwater conditions, erosion may not be a serious problem. The designer should determine if the tailwater will always control or if the outlet will be unsubmerged under some circumstances. Full flow can also exist when the discharge is high enough to produce critical depth equal to or higher than the crown of the culvert barrel. As long as critical depth is higher than the crown, outlet velocity reduction can be achieved by increasing the barrel size as illustrated above.
In Figures 3.1A, B, and C, the tailwater is below the crown of the culvert. Outlet velocity is determined using the flow area at the outlet that is calculated using the higher of the tailwater or critical depth. For Figure 3.1B, the tailwater controls; for Figures 3.1A and 3.1C, critical depth controls. (Appendix B includes useful figures for estimating critical depth for a variety of culvert shapes.) If critical depth is above the culvert, the culvert will flow full and the outlet velocity can be reduced by increasing the culvert size as shown above. The following example illustrates critical depth and velocity computation for full and partial full flow at the outlet.
Design Example: Velocity Reduction by Increasing Culvert Size When Critical Depth Occurs at the Outlet (SI)
Evaluate the reduction in velocity by replacing a 914 mm diameter culvert with a 1219 mm diameter culvert. Given:
Solution
Step 1. Read critical depth, y_{c}, for 900 mm CMP from Figure B.2. Since y_{c} exceeds 0.900 m, the barrel is flowing full to the end even though TW is less than 0.900 m.
Step 2. Calculate flow area, A, and velocity, V, with the pipe flowing full.
A = πD^{2}/4 = 3.14(0.900)^{2}/4 = 0.636 m^{2}
V = Q/A = 2.83/0.656 = 4.4 m/s.
Step 3. Read critical depth, y_{c}, for 1200 mm CMP from Figure B.2. The new y_{c} = 0.95 m which is less than D so y_{c} controls outlet velocity.
Step 4. Calculate flow area, A, using Table B.2. With y/D = 0.95/1.2 = 0.79, A/D^{2} = 0.6655, and V = Q/A = 2.832/(0.6655 (1.2)^{2}) = 2.95 m/s.
This is a reduction of about 32 percent. The reduction is less than shown in Table 3.1 because the 1.2 m pipe is not flowing full at the exit.
Design Example: Velocity Reduction by Increasing Culvert Size When Critical Depth Occurs at the Outlet (CU)
Evaluate the reduction in velocity by replacing a 3ftdiameter culvert with a 4ftdiameter culvert. Given:
Solution
Step 1. Read critical depth, y_{c}, for 3 ft CMP from Figure B.2. Since y_{c} exceeds 3 ft, the barrel is flowing full to the end even though TW is less than 3 ft.
Step 2. Calculate flow area, A, and velocity, V, with the pipe flowing full.
A = πD^{2}/4 = 3.14(3)^{2}/4 = 7.065 ft^{2}
V = Q/A = 100/7.065 = 14.2 ft/s.
Step 3. Read critical depth, y_{c}, for 4 ft CMP from Figure B.2. The new y_{c} = 3.1 ft which is less than 4 ft so y_{c} controls outlet velocity.
Step 4. Calculate flow area, A, using Table B.2. With y/D = 3.1/4 = 0.78, A/D^{2} = 0.6573, and V = Q/A = 100/0.6573(4)^{2} = 9.5 ft/s.
This is a reduction of about 33 percent. The reduction is less than shown in Table 3.1 because the 4 ft pipe is not flowing full at the exit.
Brink depth, y_{o}, which is shown in Figure 3.2, is the depth that occurs at the exit of the culvert. The flow goes through critical depth upstream of the outlet when the tailwater elevation is below the critical depth elevation in the culvert. Figures 3.3 and 3.4 may be used to determine outlet brink depths for rectangular and circular sections. These figures are dimensionless rating curves that indicate the effect on brink depth of tailwater for culverts on mild or horizontal slopes. In order to use these curves, the designer must determine normal depth or tailwater (TW) in the outlet channel and Q/(BD^{3/2}) or Q/D^{5/2} for the culvert. Table B.1 (Appendix B) can be used to estimate TW if the downstream channel can be approximated with a trapezoidal channel.
For culvert shapes other than rectangular and circular, the brink depth for low tailwater can be approximated from the critical depth curves found in Appendix B. Since critical depth is larger than brink depth, determining brink depth in this manner is not conservative, but is acceptable.
Figure 3.2. Definition Sketch for Brink Depth.
When the tailwater depth is low, culverts on mild or horizontal slopes will flow with critical depth near the outlet. This is indicated on the ordinate of Figures 3.3 and 3.4. As the tailwater increases, the depth at the brink increases at a variable rate along the Q/(BD^{3/2}) or Q/D^{5/2}curve, until a point where the tailwater and brink depth vary linearly at the 45^{o} line on the figures. The following example illustrates the use of these figures and the effect of changing culvert size for a constant Q and TW.
Design Example: Velocity Reduction by Increasing Culvert Size for Brink Depth Conditions (SI)
Evaluate the reduction in velocity by replacing a 1.050 m pipe culvert with a larger pipe culvert. Given:
Solution
Step 1. Calculate the quantity K_{u}Q/D^{5/2} and TW/D. From Figure 3.4 determine y_{o}/D. (See following table for calculations.)
Step 2. Calculate y_{c} from Figure B.2 or other appropriate method. Note that critical depth is greater than brink depth.
Step 3. Determine flow area based on y_{o}/D using Table B.2 and outlet velocity.
D (m)  1.811Q/D^{5/2}  TW/D  y_{o}/D  y_{o} (m)  y_{c} (m)  A/D^{2}  A (m^{2})  V=Q/A (m/s) 

1.050  2.73  0.58  0.64  0.67  0.73  0.5308  0.585  2.90 
1.200  1.95  0.51  0.55  0.66  0.70  0.4426  0.637  2.67 
1.350  1.45  0.45  0.47  0.63  0.70  0.3627  0.661  2.57 
1.500  1.12  0.41  0.42  0.63  0.67  0.3130  0.704  2.41 
Changing culvert diameter from 1.050 to 1.500 m, a 43 percent increase, results in a decrease of only 17 percent in the outlet velocity.
Figure 3.3. Dimensionless Rating Curves for the Outlets of Rectangular Culverts on Horizontal and Mild Slopes (Simons, 1970)
Figure 3.4. Dimensionless Rating Curves for the Outlets of Circular Culverts on Horizontal and Mild Slopes (Simons, 1970)
Design Example: Velocity Reduction by Increasing Culvert Size for Brink Depth Conditions CU)
Evaluate the reduction in velocity by replacing a 3.5 ft pipe culvert with a larger pipe culvert. Given:
Solution
Step 1. Calculate the quantity K_{u}Q/D^{5/2} and TW/D. From Figure 3.4 determine y_{o}/D. (See following table for calculations.)
Step 2. Calculate y_{c} from Figure B.2 or other appropriate method. Note that critical depth is greater than brink depth.
Step 3. Determine flow area based on y_{o}/D using Table B.2 and outlet velocity.
D (ft)  1.811Q/D^{5/2}  TW/D  y_{o}/D  y_{o} (ft)  y_{c} (ft)  A/D^{2}  A (ft^{2})  V=Q/A (ft/s) 

3.5  2.62  0.57  0.63  2.20  2.4  0.52  6.4  9.4 
4.0  1.88  0.50  0.54  2.16  2.3  0.43  6.9  8.7 
4.5  1.40  0.44  0.46  0.2.10  2.3  0.35  7.1  8.5 
5.0  1.07  0.40  0.41  2.05  2.2  0.30  7.5  8.0 
Changing culvert diameter from 3.5 to 5 ft, a 43 percent increase, results in a decrease of only 15 percent in the outlet velocity.
Figure 3.5 (Normann, et al., 2001) shows the types of flow for culverts on steep slopes, i.e., culverts flowing with inlet control.
For culvert flow types shown in Figure 3.5B and D, full flow is assumed at the outlet. The outlet velocity is calculated using the full barrel area. See Section 3.1.1 for a discussion on the effect of increasing culvert diameter to decrease outlet velocity.
For culvert flow types shown in Figure 3.5A and C, normal flow is assumed at the culvert outlet and the outlet velocity is computed using Manning's Equation. Hydraulic Design Series No. 3 (FHWA, 1961) provides charts for a direct solution of Manning's Equation for circular and rectangular culverts. Tables B.1 and B.2 (Appendix B) can also be used to determine normal depth for circular and rectangular culverts. The following example illustrates how to compute normal depth and the effect on outlet velocity of increasing the roughness of the culvert.
Figure 3.5. Inlet Control Flow Types
Design Example: Increasing Roughness to Reduce Velocity (SI)
Evaluate increasing roughness for reducing velocity. Given:
Solution
For a smooth pipe (concrete):
Step 1. Calculate the quantity αQn/(D^{8/3}S^{1/2}) = 1.49(2.832)(0.012)/((1.524)^{8/3}(0.01)^{1/2}) = 0.1646
Step 2. Calculate depth, y, from Table B.2. y/D = 0.41, y = 0.41(1.524) = 0.625 m
Step 3. Calculate area, A, from Table B.2. A/D^{2} = 0.3032, A = 0.3032(1.524)^{2} = 0.704 m^{2}
Step 4. Calculate velocity, V_{o}, = Q/A = 2.832/0.704 = 4.02 m/s.
Step 5. Read critical depth, y_{c}, from Figure B.2. y_{c} = 0.9 m.
Since y_{c} > y, the flow is supercritical and exit depth is normal depth.
For a rough pipe (corrugated metal):
Step 1. Calculate αQn/(D^{8/3}S^{1/2}) = 1.49(2.832)(0.024)/((1.524)^{8/3}(0.01)^{1/2}) = 0.3293
Step 2. Calculate depth, y, from Table B.2. y/D = 0.62, y = 0.62(1.524) = 0.945 m
Step 3. Calculate area, A, from Table B.2. A/D^{2} = 0.5115, A = 0.5115(1.524)^{2} = 1.19 m^{2}
Step 4. Calculate velocity, V_{o}, = Q/A = 2.832/1.19 = 2.38 m/s.
Step 5. Read critical depth, y_{c}, from Figure B.2. y_{c} = 0.9 m.
Since y_{c} < y, the flow is subcritical. The exit depth will be critical depth of 0.9 m and the exit velocity will be critical velocity of 2.41 m/s.
Design Example: Increasing Roughness to Reduce Velocity (CU)
Evaluate increasing roughness for reducing velocity. Given:
Solution
For a smooth pipe (concrete):
Step 1. Calculate the quantity αQn/(D^{8/3}S^{1/2}) = 1(100)(0.012)/((5)^{8/3}(0.01)^{1/2}) = 0.1642
Step 2. Calculate depth, y, from Table B.2. y/D = 0.41, y = 0.41(5) = 2.05 ft
Step 3. Calculate area, A, from Table B.2. A/D^{2} = 0.3032, A = 0.3032(5)^{2} = 7.58 ft^{2}
Step 4. Calculate velocity, V_{o}, = Q/A = 100/7.58 = 13.2 ft/s.
Step 5. Read critical depth, y_{c}, from Figure B.2. y_{c} = 2.9 ft. Since y_{c} > y, the flow is supercritical and exit depth is normal depth.
For a rough pipe (corrugated metal):
Step 1. Calculate αQn/(D^{8/3}S^{1/2}) = 1(100)(0.024)/((5)^{8/3}(0.01)^{1/2}) = 0.3283
Step 2. Calculate depth, y, from Table B.2. y/D = 0.62, y = 0.62(5) = 3.1 ft
Step 3. Calculate area, A, from Table B.2. A/D^{2} = 0.5115, A = 0.5115(5)^{2} = 12.78 ft^{2}
Step 4. Calculate velocity, V_{o}, = Q/A = 100/12.78 = 7.82 ft/s.
Step 5. Read critical depth, y_{c}, from Figure B.2. y_{c} = 2.9 ft. Since y_{c} < y, the flow is subcritical. The exit depth will be critical depth of 2.9 ft and the exit velocity will be critical velocity of 7.9 ft/s.
For culverts on steep slopes, increasing the barrel size for a given discharge and slope has little effect on velocity. For example, using the 1.524 m (5 ft) diameter concrete pipe in the previous example, a V_{o} = 4.02 m/s (13.2 ft/s) was calculated. If a 2.438 m (8 ft) pipe is put at the same location, the velocity in the larger pipe will be 3.84 m/s (12.6 ft/s). The pipe diameter was more than doubled, but the velocity was only decreased by 4 percent.
Some reduction in outlet velocity can be obtained by increasing the number of barrels carrying the total discharge. Reducing the flow rate per barrel reduces velocity at normal depth if the flow line slopes are the same. Substituting two smaller pipes with the same depth to diameter ratio for a large one reduces Q per barrel to onehalf the original rate and the outlet velocity to approximately 87 percent of that in the singlebarrel design. However, this 13 percent reduction must be considered in light of the increased cost of the culverts. In addition, the percentage reduction decreases as the number of barrels is increased. For example, using four pipes instead of three provides only an additional 5 percent reduction in outlet velocity. A design using more barrels may still result in velocities requiring protection, with a large increase in the area to be protected.
For culverts on slopes greater than critical, rougher material will cause greater depth of flow and less velocity in equal size pipes. Velocity varies inversely with resistance; therefore, using a corrugated metal pipe instead of a concrete pipe will reduce velocity approximately 40 percent, and substitution of a structural plate corrugated metal pipe for concrete will result in about 50 percent reduction in velocity. Barrel resistance is obviously an important factor in reducing velocity at the outlets of culverts on steep slopes. Chapter 7 contains detailed discussion and specific design information for increasing barrel resistance.
Substituting a "brokenslope" flow line for a steep, continuous slope can be used for controlling outlet velocity. Chapter 7 contains detailed discussion and specific design information for designing brokenback culverts.
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Cynthia Nurmi
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