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FHWA > Engineering > Hydraulics > HEC 14 > Chapter 8 
Hydraulic Design of Energy Dissipators for Culverts and Channels

Stilling Basin  Minimum Approach Froude Number  Maximum Approach Froude Number 

USBR Type III  4.5  17 
USBR Type IV  2.5  4.5 
SAF  1.7  17 
The selection of a stilling basin depends on several considerations including hydraulic limitations, constructibility, basin size, and cost. The design examples in this chapter all use the identical site conditions to provide a comparison between the size of basins and a free hydraulic jump basin for one case. Table 8.2 summarizes the results of these examples with the incoming Froude number, the required tailwater at the exit of the basin along with basin length and depth. For this example, the SAF stilling basin results in the shortest and shallowest basin. Details of the design procedures and this design example are found in the following sections.
Basin Type^{1}  Froude Number  Required Tailwater^{3}, m (ft)  Basin Length,m (ft)  Basin Depth,m (ft) 

Free jump  7.6  3.1 (10.1)  33.7 (109.2)  4.8 (15.5) 
USBR Type III  6.9  3.0 (9.6)  20.6 (67.3)  3.8 (12.5) 
USBR Type IV^{2}  8.0  3.5 (11.2)  38.1 (121.8)  5.5 (17.4) 
SAF  6.1  2.4 (7.9)  12.4 (39.7)  2.7 (8.6) 
^{1}Based on a 3 m by 1.8 m (10 ft by 6 ft) box culvert at a design discharge of 11.8 m^{3}/s (417 ft^{3}/s). All basins have a constant width equal to the culvert width. Detailed description of the example is found in Section 8.1.  
^{2}The USBR Type IV approach Froude number is outside of the recommended range, but was included for comparison.  
^{3}Required tailwater influences basin depth. Velocity leaving each of these basins is the same and depends on the tailwater channel. 
As explained in Chapter 4, the higher the Froude number at the entrance to a basin, the more efficient the hydraulic jump and the shorter the resulting basin. To increase the Froude number as the water flows from the culvert to the basin, an expansion and depression is used as is shown in Figure 8.1. The expansion and depression converts depth, or potential energy, into kinetic energy by allowing the flow to expand, drop, or both. The result is that the depth decreases and the velocity and Froude number increase.
Figure 8.1. Definition Sketch for Stilling Basin
The Froude number used to determine jump efficiency and to evaluate the suitability of alternative stilling basins as described in Table 8.1 is defined in Equation 8.1.
(8.1)where,
Fr_{1} = Froude number at the entrance to the basin
V_{1} = velocity entering the basin, m/s (ft/s)
y_{1} = depth entering the basin, m (ft)
g = acceleration due to gravity, m/s^{2} (ft/s^{2})
To solve for the velocity and depth entering the basin, the energy balance is written from the culvert outlet to the basin. Substituting Q/(y_{1}W_{B}) for V_{1} and solving for Q results in:
(8.2)where,
W_{B} = width of the basin, m/s (ft/s)
V_{o} = culvert outlet velocity, m/s (ft/s)
y_{1} = depth entering the basin, m (ft)
y_{o} = culvert outlet depth, m (ft)
z_{1} = ground elevation at the basin entrance, m (ft)
z_{o} = ground elevation at the culvert outlet, m (ft)
Equation 8.2 has three unknowns y_{1}, W_{B}, and z_{1}. The depth y_{1} can be determined by trial and error if W_{B} and z_{1} are assumed. W_{B} should be limited to the width that a jet would flare naturally in the slope distance L.
(8.3)where,
L_{T} = length of transition from culvert outlet to basin, m (ft)
S_{T} = slope of the transition, m/m (ft/ft)
Fr_{o} = outlet Froude number
Since the flow is supercritical, the trial y_{1} value should start near zero and increase until the design Q is reached. This depth, y_{1}, is used to find the sequent (conjugate) depth, y_{2}, using the hydraulic jump equation:
(8.4)where,
y_{2} = conjugate depth, m (ft)
y_{1} = depth approaching the jump, m (ft)
C = ratio of tailwater to conjugate depth, TW/y_{2}
Fr_{1} = approach Froude number
For a free hydraulic jump, C = 1.0. Later sections on the individual stilling basin types provide guidance on the value of C for those basins. For the jump to occur, the value of y_{2} + z_{2} must be equal to or less than TW + z_{3} as shown in Figure 8.1. If z_{2} + y_{2} is greater than z_{3} +TW, the basin must be lowered and the trial and error process repeated until sufficient tailwater exists to force the jump.
In order to perform this check, z_{3} and the basin lengths must be determined. The length of the transition is calculated from:
(8.5)where,
L_{T} = length of the transition from the culvert outlet to the bottom of the basin, m (ft)
S_{T} = slope of the transition entering the basin, m/m (ft/ft)
The length of the basin, L_{B}, depends on the type of basin, the entrance flow depth, y_{1}, and the entrance Froude number, Fr_{1}. Figure 8.2 describes these relationships for the free hydraulic jump as well as several USBR stilling basins.
Figure 8.2. Length of Hydraulic Jump on a Horizontal Floor
The length of the basin from the floor to the sill is calculated from:
(8.6)where,
L_{S} = length of the basin from the bottom of the basin to the basin exit (sill), m (ft)
S_{S} = slope leaving the basin, m/m (ft/ft)
The elevation at the entrance to the tailwater channel is then calculated from:
(8.7)where,
z_{3} = elevation of basin at basin exit (sill), m (ft)
Figure 8.1 also illustrates a radius of curvature between the culvert outlet and the transition to the stilling basin. If the transition slope is 0.5V:1H or steeper, use a circular curve at the transition with a radius defined by Equation 8.8 (Meshgin and Moore, 1970). It is also advisable to use the same curved transition going from the transition slope to the stilling basin floor.
(8.8)where,
r = radius of the curved transition, m (ft)
Fr = Froude number
y = depth approaching the curvature, m (ft)
For the curvature between the culvert outlet and the transition, the Froude number and depth are taken at the culvert outlet. For the curvature between the transition and the stilling basin floor, the Froude number and depth are taken as Fr_{1} and y_{1}.
The design procedure for all of these stilling basins may be summarized in the following steps. Basin specific variations to these steps are discussed in the following sections on each basin.
Step 1. Determine the velocity and depth at the culvert outlet. For the culvert outlet, calculate culvert brink depth, y_{o}, velocity, V_{o}, and Fr_{o}. For subcritical flow, use Figure 3.3 or Figure 3.4. For supercritical flow, use normal depth in the culvert for y_{o}. (See HDS 5 (Normann, et al., 2001) for additional information on culvert brink depths.)
Step 2. Determine the velocity and TW depth in the receiving channel downstream of the basin. Normal depth may be determined using Table B.1 or other appropriate technique.
Step 3. Estimate the conjugate depth for the culvert outlet conditions using Equation 8.4 to determine if a basin is needed. Substitute y_{o} and Fr_{o} for y_{1} and Fr_{1}, respectively. The value of C is dependent, in part, on the type of stilling basin to be designed. However, in this step the occurrence of a free hydraulic jump without a basin is considered so a value of 1.0 is used. Compare y_{2} and TW. If y_{2} < TW, there is sufficient tailwater and a jump will form without a basin. The remaining steps are unnecessary.
Step 4. If step 3 indicates a basin is needed (y_{2} > TW), make a trial estimate of the basin bottom elevation, z_{1}, a basin width, W_{B}, and slopes S_{T} and S_{S}. A slope of 0.5 (0.5V:1H) or 0.33 (0.33V:1H) is satisfactory for both S_{T} and S_{s}. Confirm that W_{B} is within acceptable limits using Equation 8.3. Determine the velocity and depth conditions entering the basin and calculate the Froude number. Select candidate basins based on this Froude number.
Step 5. Calculate the conjugate depth for the hydraulic conditions entering the basin using Equation 8.4 and determine the basin length and exit elevation. Basin length and exit elevation are computed using Equations 8.5, 8.6, and 8.7 as well as Figure 8.2. Verify that sufficient tailwater exists to force the hydraulic jump. If the tailwater is insufficient go back to step 4. If excess tailwater exists, the designer may either go on to step 6 or return to step 4 and try a shallower (and smaller) basin.
Step 6. Determine the needed radius of curvature for the slope changes entering the basin using Equation 8.8.
Step 7. Size the basin elements for basin types other than a free hydraulic jump basin. The details for this process differ for each basin and are included in the individual basin sections.
Design Example: Stilling Basin with Free Hydraulic Jump (SI)
Find the dimensions for a stilling basin (see Figure 8.1) with a free hydraulic jump providing energy dissipation for a reinforced concrete box culvert. Given:
Solution
Step 1. Determine the velocity and depth at the culvert outlet. By trial and error using Manning's Equation, the normal depth is calculated as:
V_{o} = 8.50 m/s, y_{o} = 0.463 m
Since the Froude number is greater than 1.0, the normal depth is supercritical and the normal depth is taken as the brink depth.
Step 2. Determine the velocity and depth (TW) in the receiving channel. By trial and error using Manning's Equation or by using Table B.1:
V_{n} = 4.84 m/s, y_{n} = TW = 0.574 m
Step 3. Estimate the conjugate depth for the culvert outlet conditions using Equation 8.4. C = 1.0.
Since y_{2} (2.4 m) > TW (0.574 m) a jump will not form and a basin is needed.
Step 4. Since y_{2}  TW = 2.64  0.574 = 2.07 m, try z_{1} = z_{o}  2.07 = 28.4 m
Also, choose W_{B} = 3.0 m (no expansion from culvert to basin) and slopes S_{T} = 0.5 and S_{S }= 0.5.
Check W_{B} using Equation 8.3, but first calculate the transition length from Equation 8.5.
W_{B} is OK 
By using Equation 8.2 or other appropriate method by trial and error, the velocity and depth conditions entering the basin are:
V_{1} = 10.74 m/s, y_{1} = 0.366 m
Step 5. Calculate the conjugate depth for a free hydraulic jump (C=1) using Equation 8.4.
From Figure 8.2 basin length, L_{B}/y_{2} = 6.1. Therefore, L_{B} = 6.1(2.77) = 16.9 m.
The length of the basin from the floor to the sill is calculated from Equation 8.6:
The elevation at the entrance to the tailwater channel is from Equation 8.7:
Since y_{2} +z_{2} (2.77+28.4) > z_{3} + TW (29.05+ 0.574), tailwater is not sufficient to force a jump in the basin. Go back to step 4.
Step 4 (2nd iteration). Try z_{1} = 25.7 m. Maintain W_{B}, S_{T}, and S_{S}.
By using Equation 8.2 or other appropriate method by trial and error, the velocity and depth conditions entering the basin are:
V_{1} = 13.02 m/s, y_{1} = 0.302 m
Step 5 (2nd iteration). Calculate the conjugate depth for a free hydraulic jump (C=1) using Equation 8.4.
From Figure 8.2 basin length, L_{B}/y_{2} = 6.1. Therefore, L_{B} = 6.1(3.10) = 18.9 m.
The length of the basin from the floor to the sill is calculated from Equation 8.6:
The elevation at the entrance to the tailwater channel is from Equation 8.7:
Since y_{2} +z_{2} (3.10+25.7) < z_{3} + TW (28.30+ 0.574), tailwater is sufficient to force a jump in the basin. Continue on to step 6.
Step 6. For the slope change from the outlet to the transition, determine the needed radius of curvature using Equation 8.8 and the results from step 1.
Step 7. Size the basin elements. Since this is a free hydraulic jump basin, there are no additional elements and the design is complete. The basin is shown in the following sketch.
Total basin length = 9.6 + 18.9 + 5.2 = 33.7 m
Sketch for Free Hydraulic Jump Stilling Basin Design Example (SI)
Design Example: Stilling Basin with Free Hydraulic Jump (CU)
Find the dimensions for a stilling basin (see Figure 8.1) with a free hydraulic jump providing energy dissipation for a reinforced concrete box culvert. Given:
Solution
Step 1. Determine the velocity and depth at the culvert outlet. By trial and error using Manning's Equation, the normal depth is calculated as:
V_{o} = 27.8 ft/s, y_{o} = 1.50 ft
Since the Froude number is greater than 1.0, the normal depth is supercritical and the normal depth is taken as the brink depth.
Step 2. Determine the velocity and depth (TW) in the receiving channel. By trial and error using Manning's Equation or by using Table B.1:
V_{n} = 15.9 ft/s, y_{n} = TW = 1.88 ft
Step 3. Estimate the conjugate depth for the culvert outlet conditions using Equation 8.4. C = 1.0.
Since y_{2} (7.8 ft) > TW (1.88 ft) a jump will not form and a basin is needed.
Step 4. Since y_{2}  TW = 8.55  1.88 = 6.67 ft, try z_{1} = z_{o} 6.67 = 93.3 ft, use 93.
Also, choose W_{B} = 10.0 ft (no expansion from culvert to basin) and slopes S_{T} = 0.5 and S_{S }= 0.5.
Check W_{B} using Equation 8.3, but first calculate the transition length from Equation 8.5.
; W_{B} is OK 
By using Equation 8.2 or other appropriate method by trial and error, the velocity and depth conditions entering the basin are:
V_{1} = 35.3 ft/s, y_{1} = 1.18 ft
Step 5. Calculate the conjugate depth for a free hydraulic jump (C=1) using Equation 8.4.
From Figure 8.2 basin length, L_{B}/y_{2} = 6.1. Therefore, L_{B} = 6.1(8.94) = 54.5 ft.
The length of the basin from the floor to the sill is calculated from Equation 8.6:
The elevation at the entrance to the tailwater channel is from Equation 8.7:
Since y_{2} +z_{2} (8.94+93) > z_{3} + TW (95.25+1.88), tailwater is not sufficient to force a jump in the basin. Go back to step 4.
Step 4 (2nd iteration). Try z_{1} = 84.5 ft. Maintain W_{B}, S_{T}, and S_{S}.
By using Equation 8.2 or other appropriate method by trial and error, the velocity and depth conditions entering the basin are:
V_{1} = 42.5 ft/s, y_{1} = 0.98 ft
Step 5 (2nd iteration). Calculate the conjugate depth for a free hydraulic jump (C=1) using Equation 8.4.
From Figure 8.2 basin length, L_{B}/y_{2} = 6.1. Therefore, L_{B} = 6.1(10.07) = 61.4 ft.
The length of the basin from the floor to the sill is calculated from Equation 8.6:
The elevation at the entrance to the tailwater channel is from Equation 8.7:
Since y_{2} + z_{2} (10.1 + 84.5) < z_{3} + TW (92.90 + 1.88), tailwater is sufficient to force a jump in the basin. Continue on to step 6.
Step 6. For the slope change from the outlet to the transition, determine the needed radius of curvature using Equation 8.8 and the results from step 1.
Step 7. Size the basin elements. Since this is a free hydraulic jump basin, there are no additional elements and the design is complete. The basin is shown in the following sketch.
Total basin length = 31.0 + 61.4 + 16.8 = 109.2 ft
Sketch for Free Hydraulic Jump Stilling Basin Design Example (CU)
The USBR Type III stilling basin (USBR, 1987) employs chute blocks, baffle blocks, and an end sill as shown in Figure 8.3. The basin action is very stable with a steep jump front and less wave action downstream than with the free hydraulic jump. The position, height, and spacing of the baffle blocks as recommended below should be adhered to carefully. If the baffle blocks are too far upstream, wave action in the basin will result; if too far downstream, a longer basin will be required; if too high, waves can be produced; and, if too low, jump sweep out or rough water may result.
The baffle blocks may be shaped as shown in Figure 8.3 or cubes; both are effective. The corners should not be rounded as this reduces energy dissipation.
The recommended design is limited to the following conditions:
Figure 8.3. USBR Type III Stilling Basin
The general design procedure outlined in Section 8.1 applies to the USBR Type III stilling basin. Steps 1 through 4 and step 6 are applied without modification. For step 5, two adaptations to the general design procedure are made:
For step 7, sizing the basin elements (chute blocks, baffle blocks, and an end sill), the following guidance is recommended. The height of the chute blocks, h_{1}, is set equal to y_{1}. If y_{1} is less than 0.2 m (0.66 ft), then h_{1} = 0.2 m (0.66 ft).
The number of chute blocks is determined by Equation 8.9 rounded to the nearest integer.
(8.9)where,
N_{c} = number of chute blocks
Block width and block spacing are determined by:
(8.10)where,
W_{1} = block width, m (ft)
W_{2} = block spacing, m (ft)
Equations 8.9 and 8.10 will provide N_{c} blocks and N_{c}1 spaces between those blocks. The remaining basin width is divided equally for spaces between the outside blocks and the basin sidewalls. With these equations, the height, width, and spacing of chute blocks should approximately equal the depth of flow entering the basin, y_{1}. The block width and spacing may be reduced as long as W_{1} continues to equal W_{2}.
The height, width, and spacing of the baffle blocks are shown on Figure 8.3. The height of the baffles is computed from the following equation:
(8.11)where,
h_{3} = height of the baffle blocks, m (ft)
The top thickness of the baffle blocks should be set at 0.2h_{3} with the back slope of the block on a 1:1 slope. The number of baffle blocks is as follows:
(8.12)where,
N_{B} = number of baffle blocks (rounded to an integer)
Baffle width and spacing are determined by:
(8.13)where,
W_{3} = baffle width, m (ft)
W_{4} = baffle spacing, m (ft)
As with the chute blocks, Equations 8.12 and 8.13 will provide N_{B} baffles and N_{B}1 spaces between those baffles. The remaining basin width is divided equally for spaces between the outside baffles and the basin sidewalls. The width and spacing of the baffles may be reduced for narrow structures provided both are reduced by the same amount. The distance from the downstream face of the chute blocks to the upstream face of the baffle block should be 0.8y_{2}.
The height of the final basin element, the end sill, is given as:
(8.14)where,
h_{4} = height of the end sill, m (ft)
The fore slope of the end sill should be set at 0.5:1 (V:H).
If these recommendations are followed, a short, compact basin with good dissipation action will result. If they cannot be followed closely, a model study is recommended.
Design Example: USBR Type III Stilling Basin (SI)
Design a USBR Type III stilling basin for a reinforced concrete box culvert. Given:
Solution
The culvert, design discharge, and tailwater channel are the same as considered for the free hydraulic jump stilling basin addressed in the design example in Section 8.1. Steps 1 through 3 of the general design process are identical for this example so they are not repeated here. The tailwater depth from the previous design example is TW=0.574 m.
Step 4. Try z_{1} = 26.7 m. W_{B} = 3.0 m, S_{T} = 0.5 m/m, and S_{S} = 0.5 m/m. From Equation 8.5:
By using Equation 8.2 or other appropriate method by trial and error, the velocity and depth conditions entering the basin are:
V_{1} = 12.2 m/s, y_{1} = 0.322 m
Step 5. Calculate the conjugate depth in the basin (C=1) using Equation 8.4.
From Figure 8.2 basin length, L_{B}/y_{2} = 2.7. Therefore, L_{B} = 2.7(2.98) = 8.0 m.
The length of the basin from the floor to the sill is calculated from Equation 8.6:
The elevation at the entrance to the tailwater channel is from Equation 8.7:
Since y_{2} +z_{2} (2.98+26.7) < z_{3} + TW (29.15+ 0.574), tailwater is sufficient to force a jump in the basin. If the tailwater had not been sufficient, repeat step 4 with a lower assumption for z_{1}.
Step 6. Determine the needed radius of curvature for the slope changes entering the basin. See the design example Section 8.1 for this step. It is unchanged.
Step 7. Size the basin elements. For the USBR Type III basin, the elements include the chute blocks, baffle blocks, and end sill.
For the chute blocks, the height of the chute blocks, h_{1}=y_{1}=0.322 m (round to 0.32 m). The number of chute blocks is determined by Equation 8.9 and rounded to the nearest integer.
Block width and block spacing are determined by Equation 8.10:
With 5 blocks at 0.30 m and 4 spaces at 0.30 m, 0.30 m of space remains. This is divided equally for spaces between the outside blocks and the basin sidewalls.
For the baffle blocks, the height of the baffles is computed from Equation 8.11:
The number of baffles blocks is calculated from Equation 8.12:
Baffle width and spacing are determined by Equation 8.13:
With 4 baffles at 0.38 m and 3 spaces at 0.38 m, 0.34 m of space remains. This is divided equally for spaces between the outside baffles and the basin sidewalls. The distance from the downstream face of the chute blocks to the upstream face of the baffle block should be 0.8y_{2}=0.8(2.98)=2.38 m.
For the end sill, the height of the end sill is given by Equation 8.14:
Total basin length = 7.6 + 8.0 + 4.9 = 20.5 m. The basin is shown in the following sketch.
Sketch for USBR Type III Stilling Basin Design Example (SI)
Design Example: USBR Type III Stilling Basin (CU)
Design a USBR Type III stilling basin for a reinforced concrete box culvert. Given:
Solution
The culvert, design discharge, and tailwater channel are the same as considered for the free hydraulic jump stilling basin addressed in the design example in Section 8.1. Steps 1 through 3 of the general design process are identical for this example so they are not repeated here. The tailwater depth from the previous design example is TW=1.88 ft.
Step 4. Try z_{1} = 87.5 ft. W_{B} = 10.0 ft, S_{T} = 0.5 ft/ft, and S_{S} = 0.5 ft/ft. From Equation 8.5:
By using Equation 8.2 or other appropriate method by trial and error, the velocity and depth conditions entering the basin are:
V_{1} = 40.1 ft/s, y_{1} = 1.04 ft
Step 5. Calculate the conjugate depth in the basin (C=1) using Equation 8.4.
From Figure 8.2 basin length, L_{B}/y_{2} = 2.7. Therefore, L_{B} = 2.7(9.64) = 26.0 ft.
The length of the basin from the floor to the sill is calculated from Equation 8.6:
The elevation at the entrance to the tailwater channel is from Equation 8.7:
Since y_{2} +z_{2} (9.64+87.5) < z_{3} + TW (95.65+1.88), tailwater is sufficient to force a jump in the basin. If the tailwater had not been sufficient, repeat step 4 with a lower assumption for z_{1}.
Step 6. Determine the needed radius of curvature for the slope changes entering the basin. See the design example Section 8.1 for this step. It is unchanged.
Step 7. Size the basin elements. For the USBR Type III basin, the elements include the chute blocks, baffle blocks, and end sill.
For the chute blocks, the height of the chute blocks, h_{1}=y_{1}=1.04 ft (round to 1.0 ft). The number of chute blocks is determined by Equation 8.9 and rounded to the nearest integer.
Block width and block spacing are determined by Equation 8.10:
With 5 blocks at 1.0 ft and 4 spaces at 1.0 ft, 1.0 ft of space remains. This is divided equally for spaces between the outside blocks and the basin sidewalls.
For the baffle blocks, the height of the baffles is computed from Equation 8.11:
The number of baffles blocks is calculated from Equation 8.12:
Baffle width and spacing are determined by Equation 8.13:
With 4 baffles at 1.3 ft and 3 spaces at 1.3 ft, 0.9 ft of space remains. This is divided equally for spaces between the outside baffles and the basin sidewalls. The distance from the downstream face of the chute blocks to the upstream face of the baffle block should be 0.8y_{2}=0.8(9.64)=7.7 ft.
For the end sill, the height of the end sill is given by Equation 8.14:
Total basin length = 25.0 + 26.0 + 16.3 = 67.3 ft. The basin is shown in the following sketch.
Sketch for USBR Type III Stilling Basin Design Example (CU)
The USBR Type IV stilling basin (USBR, 1987) is intended for use in the Froude number range of 2.5 to 4.5. In this low Froude number range, the jump is not fully developed and downstream wave action may be a problem as discussed in Chapter 4. For the intermittent flow encountered at most highway culverts, wave action is not judged to be a severe limitation. The basin, illustrated in Figure 8.4, employs chute blocks and an end sill.
The recommended design is limited to the following conditions:
The general design procedure outlined in Section 8.1 applies to the USBR Type IV basin. Steps 1 through 4 and step 6 are applied without modification. For step 5, two adaptations to the general design procedure are made:
For step 7, sizing the basin elements (chute blocks and an end sill), the following guidance is recommended. The height of the chute blocks, h_{1}, is set equal to 2y_{1}. The top surface of the chute blocks should be sloped downstream at a 5 degree angle.
The number of chute blocks is determined by Equation 8.15a and rounded to the nearest integer.
(8.15a)where,
N_{c} = number of chute blocks
Block width and block spacing are determined by:
(8.15b) (8.15c)where,
W_{1} = block width, m (ft)
W_{2} = block spacing, m (ft)
Figure 8.4. USBR Type IV Stilling Basin
With Equation 8.14, the block width, W_{1}, should be less than or equal to the depth of the incoming flow, y_{1}. Equations 8.14 and 8.15 will provide N_{c} blocks and N_{c}1 spaces between those blocks. The remaining basin width is divided equally for spaces between the outside blocks and the basin sidewalls.
The height of the end sill, is given as:
(8.16)where,
h_{4} = height of the end sill, m (ft)
The fore slope of the end sill should be set at 0.5:1 (V:H).
Design Example: USBR Type IV Stilling Basin (SI)
Design a USBR Type IV stilling basin for a reinforced concrete box culvert. Given:
Solution
The culvert, design discharge, and tailwater channel are the same as considered for the free hydraulic jump stilling basin addressed in the design example in Section 8.1. Steps 1 through 3 of the general design process are identical for this example so they are not repeated here. The tailwater depth from the previous design example is TW=0.574 m.
Step 4. Try z_{1} = 25.00 m. W_{B}=3.0 m, S_{T}=0.5 m/m, and S_{S}=0.5 m/m. From Equation 8.5:
By using Equation 8.2 or other appropriate method by trial and error, the velocity and depth conditions entering the basin are:
V_{1} = 13.55 m/s, y_{1} = 0.290 m
It should be noted that this Froude number is outside the applicability range for the Type IV basin, therefore the Type IV is not appropriate for this situation. However, we will proceed with the calculations in order to compare basin dimensions with the other basin options.
Step 5. Calculate the conjugate depth in the basin (C=1.1) using Equation 8.4.
From Figure 8.2 basin length, L_{B}/y_{2} = 6.1. Therefore, L_{B} = 6.1(3.46) = 21.1 m.
The length of the basin from the floor to the sill is calculated from Equation 8.6:
The elevation at the entrance to the tailwater channel is from Equation 8.7:
Since y_{2} +z_{2} (3.46+25.00) < z_{3} + TW (28.00+0.574), tailwater is sufficient to force a jump in the basin. If this had not been the case, repeat step 4 with a lower assumption for z_{1}.
Step 6. Determine the needed radius of curvature for the slope changes entering the basin. See the design example Section 8.1 for this step. It is unchanged.
Step 7. Size the basin elements. For the USBR Type IV basin, the elements include the chute blocks and end sill.
For the chute blocks:
The height of the chute blocks, h_{1}=2y_{1}=2(0.290) = 0.58 m. The number of chute blocks is determined by Equation 8.15a and rounded to the nearest integer.
Block width and block spacing are determined by Equations 8.15b and 8.15c:
With 4 blocks at 0.21 m and 3 spaces at 0.53 m, 0.57 m of space remains. This is divided equally for spaces between the outside blocks and the basin sidewalls.
For the sill:
The height of the end sill, is given by Equation 8.16:
Total basin length = 11.0 + 21.1 +6.0 = 38.1 m. The basin is shown in the following sketch.
Sketch for USBR Type IV Stilling Basin Design Example (SI)
Design Example: USBR Type IV Stilling Basin (CU)
Design a USBR Type IV stilling basin for a reinforced concrete box culvert. Given:
Solution
The culvert, design discharge, and tailwater channel are the same as considered for the free hydraulic jump stilling basin addressed in the design example in Section 8.1. Steps 1 through 3 of the general design process are identical for this example so they are not repeated here. The tailwater depth from the previous design example is TW=1.88 ft.
Step 4. Try z_{1} = 82.6 ft. W_{B}=10.0 ft, S_{T}=0.5 ft/ft, and S_{S}=0.5 ft/ft. From Equation 8.5:
By using Equation 8.2 or other appropriate method by trial and error, the velocity and depth conditions entering the basin are:
V_{1} = 43.9 ft/s, y_{1} = 0.95 ft
It should bFr sub 1 equals V sub 1 divided by square root of (g times y sub 1) equals 43.9 divided by square root of (32.2 times 0.95) equals 7.9e noted that this Froude number is outside the applicability range for the Type IV basin, therefore the Type IV is not appropriate for this situation. However, we will proceed with the calculations in order to compare basin dimensions with the other basin options.
Step 5. Calculate the conjugate depth in the basin (C=1.1) using Equation 8.4.
From Figure 8.2 basin length, LB/y2 = 6.1. Therefore, LB = 6.1(11.15) = 68.0 ft.
The length of the basin from the floor to the sill is calculated from Equation 8.6:
The elevation at the entrance to the tailwater channel is from Equation 8.7:
Since y_{2} +z_{2} (11.15+82.60) < z_{3} + TW (92.10+1.88), tailwater is sufficient to force a jump in the basin. If this had not been the case, repeat step 4 with a lower assumption for z_{1}.
Step 6. Determine the needed radius of curvature for the slope changes entering the basin. See the design example Section 8.1 for this step. It is unchanged.
Step 7. Size the basin elements. For the USBR Type IV basin, the elements include the chute blocks and end sill.
For the chute blocks:
The height of the chute blocks, h_{1}=2y_{1}=2(0.95) = 1.9 ft. The number of chute blocks is determined by Equation 8.15a and rounded to the nearest integer.
Block width and block spacing are determined by Equations 8.15b and 8.15c:
With 4 blocks at 0.7 ft and 3 spaces at 1.8 ft, 1.8 ft of space remains. This is divided equally for spaces between the outside blocks and the basin sidewalls.
For the sill:
The height of the end sill, is given by Equation 8.16:
Total basin length = 34.8 + 68.0 + 19.0 = 121.8 ft. The basin is shown in the following sketch.
Sketch for USBR Type IV Stilling Basin Design Example (CU)
The Saint Anthony Falls (SAF) stilling basin, shown in Figure 8.5, provides chute blocks, baffle blocks, and an end sill that allows the basin to be shorter than a free hydraulic jump basin. It is recommended for use at small structures such as spillways, outlet works, and canals where the Froude number at the dissipator entrance is between 1.7 and 17. The reduction in basin length achieved through the use of appurtenances is about 80 percent of the free hydraulic jump length. The SAF stilling basin provides an economical method of dissipating energy and preventing stream bed erosion.
Figure 8.5. SAF Stilling Basin (Blaisdell, 1959)
The general design procedure outlined in Section 8.1 applies to the SAF stilling basin. Steps 1 through 3 and step 6 are applied without modification. As part of step 4, the designer selects a basin width, W_{B}. For box culverts, W_{B} must equal the culvert width, W_{o}. For circular culverts, the basin width is taken as the larger of the culvert diameter and the value calculated according to the following equation:
(8.17)where,
W_{B} = basin width, m (ft)
Q = design discharge, m^{3}/s (ft^{3}/s)
D_{o} = culvert diameter, m (ft)
The basin can be flared to fit an existing channel as indicated on Figure 8.5. The sidewall flare dimension z should not be greater than 0.5, i.e., 0.5:1, 0.33:1, or flatter.
For step 5, two adaptations to the general design procedure are made. First, for computing conjugate depth, C is a function of Froude number as given by the following set of equations. Depending on the Froude number, C ranges from 0.64 to 1.08 implying that the SAF basin may operate with less tailwater than the USBR basins, though tailwater is still required.
(8.18a)when 1.7 < Fr_{1 }< 5.5 
when 5.5 < Fr_{1 }< 11 
when 11 < Fr_{1 }< 17 
The second adaptation is the determination of the basin length, LB, using Equation 8.19.
(8.19)For step 7, sizing the basin elements (chute blocks, baffle blocks, and an end sill), the following guidance is recommended. The height of the chute blocks, h_{1}, is set equal to y_{1}.
The number of chute blocks is determined by Equation 8.20 rounded to the nearest integer.
(8.20)where,
N_{c} = number of chute blocks
Block width and block spacing are determined by:
(8.21)where,
W_{1} = block width, m (ft)
W_{2} = block spacing, m (ft)
Equations 8.20 and 8.21 will provide N_{c} blocks and N_{c} spaces between those blocks. A half block is placed at the basin wall so there is no space at the wall.
The height, width, and spacing of the baffle blocks are shown Figure 8.5. The height of the baffles, h_{3}, is set equal to the entering flow depth, y_{1}.
The width and spacing of the baffle blocks must account for any basin flare. If the basin is flared as shown in Figure 8.5, the width of the basin at the baffle row is computed according to the following:
(8.22)where,
W_{B2} = basin width at the baffle row, m (ft)
L_{B} = basin length, m (ft)
z = basin flare, z:1 as defined in Figure 8.5 (z=0.0 for no flare)
The top thickness of the baffle blocks should be set at 0.2h_{3} with the back slope of the block on a 1:1 slope. The number of baffles blocks is as follows:
(8.23)where,
N_{B} = number of baffle blocks (rounded to an integer)
Baffle width and spacing are determined by:
(8.24)where,
W_{3} = baffle width, m (ft)
W_{4} = baffle spacing, m (ft)
Equations 8.23 and 8.24 will provide N_{B} baffles and N_{B}1 spaces between those baffles. The remaining basin width is divided equally for spaces between the outside baffles and the basin sidewalls. No baffle block should be placed closer to the sidewall than 3y_{1}/8. Verify that the percentage of W_{B2} obstructed by baffles is between 40 and 55 percent. The distance from the downstream face of the chute blocks to the upstream face of the baffle block should be L_{B}/3.
The height of the final basin element, the end sill, is given as:
(8.25)where,
h_{4} = height of the end sill, m (ft)
The fore slope of the end sill should be set at 0.5:1 (V:H). If the basin is flared the length of sill (width of the basin at the sill) is:
(8.26)where,
W_{B3} = basin width at the sill, m (ft)
L_{B} = basin length, m (ft)
z = basin flare, z:1 as defined in Figure 8.5 (z=0.0 for no flare)
Wingwalls should be equal in height and length to the stilling basin sidewalls. The top of the wingwall should have a 1H:1V slope. Flaring wingwalls are preferred to perpendicular or parallel wingwalls. The best overall conditions are obtained if the triangular wingwalls are located at an angle of 45° to the outlet centerline.
The stilling basin sidewalls may be parallel (rectangular stilling basin) or diverge as an extension of the transition sidewalls (flared stilling basin). The height of the sidewall above the floor of the basin is given by:
(8.27)where,
h_{5} = height of the sidewall, m (ft)
A cutoff wall should be used at the end of the stilling basin to prevent undermining. The depth of the cutoff wall must be greater than the maximum depth of anticipated erosion at the end of the stilling basin.
Design Example: SAF Stilling Basin (SI)
Design a SAF stilling basin with no flare for a reinforced concrete box culvert. Given:
Solution
The culvert, design discharge, and tailwater channel are the same as considered for the free hydraulic jump stilling basin addressed in the design example in Section 8.1. Steps 1 through 3 of the general design process are identical for this example so they are not repeated here. The tailwater depth from the previous design example is TW=0.574 m.
Step 4. Try z_{1} = 27.80 m. W_{B}=3.0 m (no flare), S_{T}=0.5 m/m, and S_{S}=0.5 m/m. From Equation 8.5:
By using Equation 8.2 or other appropriate method by trial and error, the velocity and depth conditions entering the basin are:
V_{1} = 11.29 m/s, y_{1} = 0.348 m
Step 5. Calculate the conjugate depth in the basin using Equation 8.4. First estimate C using Equation 8.18. For the calculated Froude number, C=0.85.
From Equation 8.19 basin length is calculated:
The length of the basin from the floor to the sill is calculated from Equation 8.6:
The elevation at the entrance to the tailwater channel is from Equation 8.7:
Z_{3} = L_{S}S_{S} + Z_{1} = 3.8(0.5) + 27.80 =29.70 m
Since y_{2} +z_{2} (2.41+27.80) < z_{3} + TW (29.70+0.574), tailwater is sufficient to force a jump in the basin. If tailwater had not been sufficient, repeat step 4 with a lower assumption for z_{1}.
Step 6. Determine the needed radius of curvature for the slope changes entering the basin. See the design example Section 8.1 for this step. It is unchanged.
Step 7. Size the basin elements. For the SAF basin, the elements include the chute blocks, baffle blocks, and an end sill.
For the chute blocks:
The height of the chute blocks, h_{1}=y_{1}=0.348 (round to 0.35 m).
The number of chute blocks is determined by Equation 8.20:
Block width and block spacing are determined by Equation 8.21:
A half block is placed at each basin wall so there is no space at the wall.
For the baffle blocks:
The height of the baffles, h_{3}=y_{1}=0.348 m. (round to 0.35 m)
The basin has no flare so the width in the basin is constant and equal to W_{B}.
The number of baffles blocks is from Equation 8.23:
Baffle width and spacing are determined from Equation 8.24. In this case W_{B2}=W_{B}.
For this design, we have 6 baffles at 0.25 m and 5 spaces between them at 0.25 m. The remaining 0.25 m is divided in half and provided as a space between the sidewall and the first baffle.
The total percentage blocked by baffles is 6(0.25)/3.0=50 percent which falls within the acceptable range of between 40 and 55 percent.
The distance from the downstream face of the chute blocks to the upstream face of the baffle block equals L_{B}/3=3.2/3=1.1 m.
For the sill:
The height of the end sill, is given in Equation 8.25:
Total basin length = 5.4 + 3.2 + 3.8 = 12.4 m. The basin is shown in the following sketch.
Sketch for SAF Stilling Basin Design Example (SI)
Design Example: SAF Stilling Basin (CU)
Design a SAF stilling basin with no flare for a reinforced concrete box culvert. Given:
Solution
The culvert, design discharge, and tailwater channel are the same as considered for the free hydraulic jump stilling basin addressed in the design example in Section 8.1. Steps 1 through 3 of the general design process are identical for this example so they are not repeated here. The tailwater depth from the previous design example is TW=1.88 ft.
Step 4. Try z_{1} = 91.40 ft. W_{B}=10.0 ft (no flare), S_{T}=0.5 ft/ft, and S_{S}=0.5 ft/ft. From Equation 8.5:
By using Equation 8.2 or other appropriate method by trial and error, the velocity and depth conditions entering the basin are:
V_{1} = 36.8 ft/s, y_{1} = 1.13 ft
Step 5. Calculate the conjugate depth in the basin using Equation 8.4. First estimate C using Equation 8.18. For the calculated Froude number, C=0.85.
From Equation 8.19 basin length is calculated:
The length of the basin from the floor to the sill is calculated from Equation 8.6:
The elevation at the entrance to the tailwater channel is from Equation 8.7:
Z_{3} = L_{S}S_{S} + Z_{1} = 12.0(0.5) + 91.40 =97.40 ft
Since y_{2} +z_{2} (7.85+91.40) < z_{3} + TW (97.40+1.88), tailwater is sufficient to force a jump in the basin. If tailwater had not been sufficient, repeat step 4 with a lower assumption for z_{1}.
Step 6. Determine the needed radius of curvature for the slope changes entering the basin. See the design example Section 8.1 for this step. It is unchanged.
Step 7. Size the basin elements. For the SAF basin, the elements include the chute blocks, baffle blocks, and an end sill.
For the chute blocks:
The height of the chute blocks, h_{1}=y_{1}=1.13 (round to 1.1 ft).
The number of chute blocks is determined by Equation 8.20:
Block width and block spacing are determined by Equation 8.21:
A half block is placed at each basin wall so there is no space at the wall.
For the baffle blocks:
The height of the baffles, h_{3}=y_{1}=1.13 ft. (round to 1.1 ft)
The basin has no flare so the width in the basin is constant and equal to W_{B}.
The number of baffles blocks is from Equation 8.23:
Baffle width and spacing are determined from Equation 8.24. In this case W_{B2}=W_{B}.
For this design, we have 6 baffles at 0.8 ft and 5 spaces between them at 0.8 ft. The remaining 1.2 ft is divided in half and provided as a space between the sidewall and the first baffle.
The total percentage blocked by baffles is 6(0.8)/10.0=48 percent which falls within the acceptable range of between 40 and 55 percent.
The distance from the downstream face of the chute blocks to the upstream face of the baffle block equals L_{B}/3=10.5/3=3.5 ft.
For the sill:
The height of the end sill, is given in Equation 8.25:
Total basin length = 17.2 + 10.5 + 12.0 = 39.7 ft. The basin is shown in the following sketch.
Sketch for SAF Stilling Basin Design Example (CU)
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