# Physical Modeling of the Scour Volume Upstream of a Slit Weir Using Uniform and Non-Uniform Mobile Beds

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{50}= 0.24, 0.55 mm and four scenarios of unsteady flow conditions at a center slit weir under different flow intensities. The steel slit weirs were built in a rectangular brick and concrete flume with dimensions of 1.25 m wide, 8.0 m long and 1.0 m deep. The dimensional analysis supports recent studies. This study demonstrates an increment in the resulted scour volume for fine and uniform sands at the center slit weir of about 2 times the value of coarse sand and 1.25 times the value measured with the side slit weir for uniform and non-uniform sands. However, the resulted scour volume for fine non-uniform sand at the center slit weir was recorded as 2.5 times that of coarse sand. There was a dramatic increase in the scour volume of about 4 times at the center slit weir and 3–3.5 at the side slit weir when the flow rate increased by 4 times.

## 1. Introduction

## 2. Materials and Methods

#### Dimensional Analysis

_{r}, $\frac{{\mathrm{d}}_{50}}{{\mathrm{d}}_{\mathrm{s}}},\frac{{\mathrm{v}}_{\mathrm{c}}}{\mathrm{V}},\frac{{\mathrm{v}}_{\mathrm{a}}}{\mathrm{V}}$. The independent variables were adopted for a non-uniform sediment size 0.24 mm at the side slit weir, with R

^{2}= 0.84, 0.985, 0.98 and 0.985, respectively.

## 3. The Experimental Work

_{50}= 0.24 mm) up to 30 cm. Then, experiments were conducted on slit weirs located at the center and at the side of the flume, and the same experiments were repeated with uniform coarse sediment (d

_{50}= 0.55 mm). However, the same sets of experiments were conducted on non-uniform fine mobile beds and then on coarser mobile beds. It is essential to highlight that the sizes of both the uniform and non-uniform sediments were identical (d

_{50}= 0.24 mm and d

_{50}= 0.55 mm).

## 4. Results

_{50}= 0.24 mm, and the other type had a median particle of d

_{50}= 0.55 mm. However, to study the effect of uniformity on the scour volume upstream of the slit weir, uniform and non-uniform sand with the same above median particles (d

_{50}= 0.24 mm and d

_{50}= 0.55 mm) were used to run the experiments with different discharges, as mentioned previously.

_{g}using the following formula [31]:

_{84}, d

_{50}and d

_{16}were determined from the grading curves shown in Figure 8 and Figure 9. However, Figure 10 and Figure 11 show the grading curves for the coarser sediment, both uniform and non-uniform.

_{g}) for the two types of the selected sand. For uniform sediment with d

_{50}= 0.24 mm, the value of σ

_{g}was 1.28, and for the sediment with d

_{50}= 0.55 mm, σ

_{g}was 1.26. However, for non-uniform sediment sizes 0.24 and 0.55 mm, the values of σ

_{g}were 1.55 and 1.6, respectively. The values of d

_{max}and d

_{min}were extracted from sediment grading curves. The following equation was used to determine d

_{50a}[31]:

_{90}was adopted as d

_{max}and d

_{50a}, and the values are presented in Table 3.

#### 4.1. Clear Water Scour

_{c}). Thus, ref. [31] specifies that the clear water scour conditions for the flow intensity should be v/v

_{c}< 1 when σ

_{g}< 1.3 for uniform sediment. In this study, the flow intensities were 0.71 and 0.84 for sediment sizes of d

_{50}= 0.55 and 0.24 mm, respectively. (v − (v

_{a}− v

_{c}))/v

_{c}< 1 and σ

_{g}> 1.3 for non-uniform sediment, which was 0.92 for a sand size of d

_{50}= 0.55 mm and 0.9 for a sand size of d

_{50}= 0.24 mm. In these flow conditions, the armor layer reduces the sour depth value, and the flow intensity ratio is replaced by v/v

_{a}.

#### 4.2. Equilibrium Scour Time

_{g}of 1.28 for uniform sand and 1.55 for a non-uniform sand size of d

_{50}= 0.24 mm and a σ

_{g}of 1.26 for uniform sand and 1.6 for a non-uniform sand size of d

_{50}= 0.55 mm. The scour hole reached equilibrium conditions after 8 h from the commencement of the experiment. The maximum scour volumes were measured with a uniform sand size of d

_{50}= 0.24 mm at the center slit weir, which was 1.1 times the one recorded for the non-uniform sediment for the same sand size. In addition, this value differs by 1.4 for the scour volume when adopting a sand size of d

_{50}= 0.55 mm. When the slit was located on the side of the weir and the sand size was d

_{50}= 0.24 mm, the value of the scour volume was 1.3 times than that of the non-uniform sand. The resulting scour volume for a sand size of d

_{50}= 0.55 mm on the upstream side of the slit weir was 24% higher than the value recorded with non-uniform sand. It is obvious in this study that the scour volume had smaller values when the sand non-uniformity increased, as mentioned in [6].

#### 4.3. Mechanism of Scour Hole Development and Velocity Distribution

_{50}= 0.24 mm and d

_{50}= 0.55 mm. Moreover, Figure 21, Figure 22, Figure 23 and Figure 24 show the comparison between the maximum scour volume under different flow intensities of 125, 95, 62, 50 and 34 L/s for sediment sizes of 0.24 and 0.55 mm with uniform and non-uniform sediment upstream of the center and side slit weirs.

_{50}= 0.24 mm with the slit located at center of the weir was reduced by 70%, and it was 78% for a sand size of d

_{50}= 0.55 mm when the flow rate changed from 125 L/s to 34 L/s. There was a 75% reduction for a non-uniform sand size of d

_{50}= 0.24 mm and a 73% reduction for a sand size of d

_{50}= 0.55 mm. The resulting scour volume at the side slit weir was minimized by 69% for a uniform sand size of d

_{50}= 0.24 mm and by 77% for a sand size of d

_{50}= 0.55 mm. However, the scour volume was reduced by 65% for a non-uniform sediment size of d

_{50}= 0.24 mm and by 79% for a sediment size of d

_{50}= 0.55 mm.

_{50}= 0.24 mm was three times that of the uniform sediment for a sand size of d

_{50}= 0.55 mm, and triple values of the scour volume were recorded for non-uniform sediment with the same median size. The behavior of the maximum scour volume was proportioned positively with the uniformity of the sand and negatively with its size.

_{sl}/B ≤ 0.3. Uniform and non-uniform sands with median particle sizes of d

_{50}= 0.24 mm and d

_{50}= 0.55 mm were adopted, as well as q

_{sl}/q < 5, v/v

_{c}and (v − (v

_{a}− v

_{c})/v

_{c}) < 1. The scour volume was measured for different slit locations (center and side). B is the channel width, b

_{sl}is the slit weir width, q is the flow rate per unit of width and q

_{sl}is the flow passing through the slit weir per unit of the weir slit width. The slope between V

_{s}. and d

_{s}was found to be three for uniform and non-uniform sediment.

^{2}thus, R

^{2}was 0.89 for uniform sediment and 0.85 for non-uniform sediment.

## 5. Conclusions

_{50}= 0.24 and 0.55. The scour volume was obtained and matched for various cases, and this study it can be concluded with the following:

- The flow rate had a major impact on the resulting scour volume. Thus, when the flow rate increased from 34 L/s to 125 L/s, the scour volume increased 4 times for a uniform sand of size d
_{50}= 0.24 mm at the center slit weir, and it was 3.25 when the slit was located at the side. For non-uniform sediment, the increment was 4 times for the same sand size at the center slit weir and three times at the side slit weir. The value of the increment in scour volume for uniform sediment with a median size of d_{50}= 0.55 mm was four times at the center slit weir. In addition, the scour volume became 4.3 times larger than the value predicted with the minimum flow rate with the side slit weir. In addition, the difference for non-uniform sediment with a sand size of d_{50}= 0.55 mm was 4 times at the center slit weir and 4.5 when the slit was at side of the weir. - The effect of the median particle size played an essential role in the scour volume upstream of the slit weir. However, the scour volume was recorded as 2 times higher when adopting a sediment particle size of 0.24 mm compared to the values measured with a sediment size of 0.55 mm for uniform sediment at the center and side slit weirs. In addition, the difference was 3 times for non-uniform sediment when the slit was at the center of the weir and by 2 at the side slit weir.
- The influence of sand uniformity was investigated in this research for the same sand median size. The scour volume resulted in a higher value with uniform sediment compared to the value obtained with non-uniform ones by 25% when the sediment size was 0.24 mm and 30% with d
_{50}= 0.55 mm. - The experimental work shows that the slit location had a governing impact on the scour volume. Higher values were recorded when the slit was positioned at the center of the weir, and the observed increment was 1.25 in the measured scour volume at the center slit weir compared to the values obtained when the slit was located at the side of the weir under the same conditions.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

d_{50} | Median particle size |

d_{s} | Scour depth |

V_{s} | Scour volume |

h_{s} | Slit weir height |

h_{w} | Weir height |

g | Gravity acceleration |

μ | Dynamic viscosity |

ρ | Water density |

ρ_{s} | Sediment density |

B | Flume width |

b_{s} | Slit weir width |

v | Flow velocity |

v_{a} | Armor velocity |

v_{c} | Sediment entrainment critical velocity |

Q | Flow rate |

y | Flow water depth |

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**Figure 1.**The relationship between the Froude number and $\frac{{\mathrm{V}}_{\mathrm{s}}^{\frac{1}{3}}}{{\mathrm{d}}_{\mathrm{s}}}$.

**Figure 2.**The relationship between $\frac{{\mathrm{d}}_{50}}{{\mathrm{d}}_{\mathrm{s}}}$ and $\frac{{\mathrm{V}}_{\mathrm{s}}^{\frac{1}{3}}}{{\mathrm{d}}_{\mathrm{s}}}$.

**Figure 3.**The relationship between $\frac{{\mathrm{v}}_{\mathrm{a}}}{\mathrm{V}}$ and $\frac{{\mathrm{V}}_{\mathrm{s}}^{\frac{1}{3}}}{{\mathrm{d}}_{\mathrm{s}}}$.

**Figure 4.**The relationship between $\frac{{\mathrm{v}}_{\mathrm{c}}}{\mathrm{V}}$ and $\frac{{\mathrm{V}}_{\mathrm{s}}^{\frac{1}{3}}}{{\mathrm{d}}_{\mathrm{s}}}$.

**Figure 8.**Grain size distribution curve for non-uniform sediment size d

_{50}= 0.24 mm and armor layer.

**Figure 10.**Grain size distribution curve for non-uniform sediment size d

_{50}= 0.55 mm and armor layer.

**Figure 12.**A Procedure used for the determination of v

_{c}for uniform sediment and v

_{c}and v

_{a}for non-uniform sediment.

**Figure 13.**Scour hole development upstream of the center slit weir: (

**a**) Leveling working section; (

**b**) Initial scour hole; (

**c**) Final scour hole reaching equilibrium conditions.

**Figure 14.**Time varying scour volume for non-uniform sediment sizes of 0.24 mm and 0.55 mm at the center slit weir.

**Figure 15.**Time varying scour volume for uniform sediment sizes of 0.24 mm and 0.55 mm at the center slit weir.

**Figure 16.**Time varying scour volume for non-uniform sediment sizes of 0.24 mm and 0.55 mm at the side slit weir.

**Figure 17.**Time varying scour volume for uniform sediment sizes of 0.24 mm and 0.55 mm at the side slit weir.

**Figure 18.**Velocity distribution along the flume: (

**a**) Velocity contour lines up to 6 m upstream of the center slit weir; (

**b**) Three-dimensional velocity distribution.

**Figure 19.**Velocity distribution along the flume: (

**a**) Velocity contour lines up to 6 m upstream of the side slit weir; (

**b**) Three-dimensional velocity distribution.

**Figure 20.**Scour by vortex action: (

**a**) Initial stage; (

**b**,

**c**) Rotating vortices with sediment release.

**Figure 21.**Scour hole contour lines under different flow intensities with the center slit weir: (

**A**) 0.24 mm; (

**B**) 0.55 mm: (a) Flow rate = 125 L/s; (b) Flow rate = 95 L/s; (c) Flow rate = 62 L/s; (d) Flow rate = 50 L/s; (e) Flow rate = 34 L/s.

**Figure 22.**Scour hole contour lines under different flow intensities with the side slit weir: (

**A**) 0.24 mm; (

**B**) 0.55 mm: (a) Flow rate = 125 L/s; (b) Flow rate = 95 L/s; (c) Flow rate = 62 L/s; (d) Flow rate = 50 L/s; (e) Flow rate = 34 L/s.

**Figure 23.**Scour hole contour lines under different flow intensities for non-uniform sediment of d

_{50}= 0.24 and 0.55 mm with the center slit weir: (

**A**) 0.24 mm; (

**B**) 0.55 mm: (a) Flow rate = 125 L/s; (b) Flow rate = 95 L/s; (c) Flow rate = 62 L/s; (d) Flow rate = 50 L/s; (e) Flow rate = 34 L/s.

**Figure 24.**Scour hole contour lines under different flow intensities for non-uniform sand of d

_{50}= 0.24 and 0.55 mm with the side slit weir: (

**A**) 0.24 mm; (

**B**) 0.55 mm: (a) Flow rate = 125 L/s; (b) Flow rate = 95 L/s; (c) Flow rate = 62 L/s; (d) Flow rate = 50 L/s; (e) Flow rate = 34 L/s.

**Figure 25.**Unsteady flow conditions for non-uniform sediment sizes of d

_{50}= 0.24 mm and 0.55 mm at the center slit weir.

**Figure 26.**Unsteady flow conditions for uniform sediment sizes of d

_{50}= 0.24 mm and 0.55 mm at the center slit weir.

**Figure 27.**Relationship between maximum scour depth and volume for non-uniform sediment sizes of d

_{50}= 0.24, 0.55 mm.

**Figure 28.**Relationship between maximum scour depth and volume for uniform sediment sizes of d

_{50}= 0.24, 0.55 mm.

**Table 1.**Studies on scour upstream, downstream and around hydraulic structures and sediment releases.

Author | Nature of Study | Main Findings |
---|---|---|

Scour development upstream and around slit weirs | ||

Ota and Sato [4] | Sediment releasing through a dam gate | Simulated the scour process around a slit weir experimentally and numerically by a 3D numerical analysis based on Reynolds-averaged Navier–Stokes (RANS) equations coupled with the VOF method and the k-ꭃ SST turbulence closure model. |

Ota [5] | 3D numerical model for a scour around a slit weir | Updated the study of Ota and Sato (2015) to reproduce the resulting scour around a slit weir. |

Ota [6] | Ordinary differential equation model for the scour upstream of a slit weir | Investigation of time varying scour volume and maximum scour depth generating upstream of a slit weir under steady and unsteady conditions by adopting an ordinary differential-equation-based model. |

Ota [7] | 3D simulation for the scour upstream of a slit weir | Suggested 3D hybrid Euler–Lagrange model for a bed-material load considering transitions between the bed load and suspended load to accurately reproduce the scour around the slit weir. |

Nkad [8] | Scour volume upstream of a slit weir | The scour volume and maximum scour depth were investigated experimentally on the upstream side of a slit weir under steady flow, clear-water scour conditions and non-uniform sedimentation. |

Scour development upstream and downstream of a submerged weir | ||

Guan [9,10] | Scour investigation upstream and downstream of a submerged weir | The scour was investigated experimentally upstream and downstream of submerged weirs within live-bed scour conditions. New equations, including the effects of sediment size, flow intensity and weir geometry are proposed for the prediction of equilibrium scour depths, and a new design method is given for estimating the maximum scour depths at the weir. |

Wang [11,12] | Local scour at the submerged weir | Experimentally studied the effect of different slopes downstream and upstream of a submerged weir on the scour within numerous scenarios for fine and coarse sediments under clear and live-bed scour conditions. The study presents a new technique for investigating the maximum scour depth and the correlation between average and maximum scour depth. |

Local scour at bed sill | ||

Gaudio [13] | Local scour downstream of a bed sill | Experimentally studied the influence of morphology on the scour downstream of a bed sill within a gravel bed with a classical dimensional analysis. The study presents numerical formulas for estimating scour depth, scour hole length and the location of the maximum scour depth. |

Marion [14] | Local scour at the bed still in high-gradient streams | Experimentally predicted the effect of steady releases of sedimentation under clear water conditions on scour depth and shape, created at the toe of the bed sills. |

Scour around bridge piers | ||

Hager [15] | Horseshoe vortex of sediment-embedded bridge piers | Experimentally investigated the flow features around a circular bridge pier. The study presents novel data for numerical simulations. |

Najafzadeh [16] | Local scour around a vertical pier in cohesive soils | An experimental work was carried out to predict the maximum scour depth generated around bridge piers under various governing parameters. The study presents a general scour depth equation and compares it with an empirical scour depth equation, and both are in good agreement. |

Ghodsi [17] | The geometric effect of complex bridge piers on the maximum scour depth | Eighty-two laboratory tests within six physical models were adopted to study pier geometry as the affecting parameter the on maximum scour depth. A dimensional analysis was carried out, and the study results clarify that each individual parameter impacts the maximum scour depth. |

Amini, Magdi and Truce [18,19,20] | Bridge scour | The majority of published studies are focused on bridge scour. |

Scour around different weir types and sediment-release techniques | ||

Dey and Barbhuiya [21,22] | Flow field in scour hole at a vertical and wing wall abutment | An experimental study was conducted to investigate the local scour and 3D flow parameters in a vertical and wing wall abutment within a clear water scour. |

Abdollahpour [23] | Erosion and sedimentation downstream of a W-weir | Experimentally studied the effect of a W-weir structure on the erosion and sedimentation of a sinusoidal channel. |

Liu [24] | Piano key weir | The PKW performance was evaluated and analyzed with new formulas for efficient discharge release. |

Khalili and Honar [25] | Simi-circular labyrinth side weir | An experimental study was conducted, evaluating a semi-circular labyrinth side weir to investigate the effect of the structure geometry on the flow intensity coefficients. |

Powell and Khan [26] | Scour upstream of a circular orifice | Investigated the sediment transport mechanism and the scour area, depth and shape upstream of a circular orifice. The investigation was conducted under steady flow conditions with different sediment sizes and heads on the orifice. |

Lauchlan [27] | Sediment transportation over weirs | Sediment transport was experimentally predicted with steep-slope weirs and dikes, including both the bed load and the suspended load. |

Zhang [28] | Local scour around submarine pipelines | An experimental work is proposed with empirical equations for accurate live bed scour predictions around submarine pipelines. |

Fathi-Moghadam [29] | Desilting of non-cohesive sediment | An experimental work is presented with numerical equations used to predict the scour cone depth and volume generated throughout the flushing process from dam intake. |

No. | Weir Location | Weir Dimensions Width (cm) × Height (cm) | Q (L/s) | Sediment Type | d_{50} (mm) | No. of Runs |
---|---|---|---|---|---|---|

Steady condition | ||||||

1 | Center | 25 × 60 | 125.0, 95.0, 62.0, 50.0, and 34.0 | Uniform | 0.24 | 5 |

2 | Center | 25 × 60 | 125.0, 95.0, 62.0, 50.0, and 34.0 | Uniform | 0.55 | 5 |

3 | Center | 25 × 60 | 125.0, 95.0, 62.0, 50.0, and 34.0 | Non- uniform | 0.24 | 5 |

4 | Center | 25 × 60 | 125.0, 95.0, 62.0, 50.0, and 34.0 | Non- uniform | 0.55 | 5 |

5 | Side | 25 × 60 | 125.0, 95.0, 62.0, 50.0, and 34.0 | Uniform | 0.24 | 5 |

6 | Side | 25 × 60 | 125.0, 95.0, 62.0, 50.0, and 34.0 | Uniform | 0.55 | 5 |

7 | Side | 25 × 60 | 125.0, 95.0, 62.0, 50.0, and 34.0 | Non- uniform | 0.24 | 5 |

8 | Side | 25 × 60 | 125.0, 95.0, 62.0, 50.0, and 34.0 | Non- uniform | 0.55 | 5 |

Unsteady condition | ||||||

9 | Center | 25 × 60 | 125.0, 62.0, 34.0 | Uniform and non- uniform | 0.24 | 2 |

10 | Center | 25 × 60 | 125.0, 62.0, 34.0 | Uniform and non- uniform | 0.55 | 2 |

Total number of test runs | 44 |

Sand Type | d_{84} (mm) | d_{50} (mm) | d_{16} (mm) | σ_{g} | d_{max} (mm) | d_{50a} (mm) | Bulk Density (kg/m^{3}) |
---|---|---|---|---|---|---|---|

Uniform sand | 0.28 | 0.24 | 0.17 | 1.28 | 0.3 | - | 1349 |

Uniform sand | 0.72 | 0.55 | 0.45 | 1.26 | 0.8 | - | 1436 |

Non- uniform sand | 0.4 | 0.24 | 0.16 | 1.55 | 0.5 | 0.3 | 1315 |

Non- uniform sand | 0.81 | 0.55 | 0.31 | 1.6 | 0.9 | 0.5 | 1518 |

No. | Scenario | Side Opening d_{50} = 0.24 mm | Center Opening d_{50} = 0.24 mm | ||
---|---|---|---|---|---|

Flat crest | Uniform sand | Non-uniform sand | Uniform sand | Non-uniform sand | |

Scour hole dimensions (x × y) cm | Scour hole dimensions (x × y) cm | Scour hole dimensions (x × y) cm | Scour hole dimensions (x × y) cm | ||

1 | Q = 125 L/s | 60 × 70 | 50 × 70 | 60 × 110 | 57 × 110 |

2 | Q = 95 L/s | 40 × 50 | 40 × 50 | 56 × 110 | 47 × 110 |

3 | Q = 62 L/s | 40 × 50 | 40 × 50 | 42 × 90 | 40 × 80 |

4 | Q = 50 L/s | 40 × 40 | 40 × 40 | 53 × 90 | 40 × 70 |

5 | Q = 34 L/s | 40 × 40 | 32 × 40 | 40 × 70 | 35 × 60 |

No. | Scenario | Side Opening d_{50} = 0.55 mm | Center Opening d_{50} = 0.55 mm | ||
---|---|---|---|---|---|

Flat crest | Uniform sand | Non-uniform sand | Uniform sand | Non-uniform sand | |

Scour hole dimensions (x × y) cm | Scour hole dimensions (x × y) cm | Scour hole dimensions (x × y) cm | Scour hole dimensions (x × y) cm | ||

1 | Q = 125 L/s | 37 × 70 | 26 × 70 | 40 × 100 | 40 × 100 |

2 | Q = 95 L/s | 37 × 70 | 25 × 60 | 40 × 100 | 35 × 100 |

3 | Q = 62 L/s | 36 × 50 | 25 × 60 | 40 × 90 | 35 × 90 |

4 | Q = 50 L/s | 36 × 50 | 24 × 50 | 40 × 90 | 32 × 90 |

5 | Q = 34 L/s | 32 × 50 | 21 × 50 | 32 × 70 | 24 × 70 |

Gaudio [13] | Marion [14] | Guan [10] | Wang [11] | Ota [6] | Nkad [8] | This Study | |
---|---|---|---|---|---|---|---|

Type of structure | Bed sills | Bed sills | Submerged weir | Submerged weir | Slit weir | Slit weir | Slit weir |

Flowrate L/s | 45–81 | 18, 22, 26 | 15–86 | 12–89.3 | 7.2 | 2.6–8 | 34–125 |

Sediment size d _{50} mm | 4.1, 8.5/uniform | 8.7 uniform | 0.26, 0.85 uniform | 0.26, 0.85 uniform | 0.22, 0.77, 1/uniform | 0.3, 0.7 non- uniform | 0.24, 0.55 uniform and non- uniform |

Number of tests | 19 | 48 | 37 | 62 | 33 | 6 | 44 |

Flume dimensions m | 2.44 wide and 0.6 deep | 10 long, 0.5 wide and 0.5 deep | 12 long, 0.44 wide and 0.58 deep | 12 long, 0.44 wide and 0.38 deep | 10.5 long, 0.5 wide and 0.35 deep | 12 long, 0.3 wide and 0.3 deep | 8 long, 1.25 wide and 1 deep |

Bed slope% | 0.0120–0.0018 | 0.042–0.041 | 0.0009–0.008 | 0.0004–0.0074 | Flat bed | Flat bed with ramp of 1:10 | Flat bed |

Flow depth cm | 9–14 | - | 12–17.4 | 15–18 | 3.6–18 | 11.1–21.1 | 18–38 |

Flow velocity m/s | 0.69–0.921 | Specific energy = water depth + $\frac{{v}^{2}}{2g}$ 7.8–10.1 | 0.281–1.124 | 0.185–1.166 | 0.13 | 0.05–0.240 | 0.15–0.26 |

Fr | 0.64–0.95 | 1.06–1.44 | 0.13–0.88 | 0.13–0.89 | 0.17 | 0.04–0.16 | 0.112–0.148 |

Maximum scour depth cm | 25.8 | 28.8 | 15.5 | 16.5 | 9.2 | 4.2 | 27 |

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## Share and Cite

**MDPI and ACS Style**

Hamdan, R.K.; Al-Adili, A.; Mohammed, T.A.
Physical Modeling of the Scour Volume Upstream of a Slit Weir Using Uniform and Non-Uniform Mobile Beds. *Water* **2022**, *14*, 3273.
https://doi.org/10.3390/w14203273

**AMA Style**

Hamdan RK, Al-Adili A, Mohammed TA.
Physical Modeling of the Scour Volume Upstream of a Slit Weir Using Uniform and Non-Uniform Mobile Beds. *Water*. 2022; 14(20):3273.
https://doi.org/10.3390/w14203273

**Chicago/Turabian Style**

Hamdan, Ruaa Khalid, Aqeel Al-Adili, and Thamer Ahmed Mohammed.
2022. "Physical Modeling of the Scour Volume Upstream of a Slit Weir Using Uniform and Non-Uniform Mobile Beds" *Water* 14, no. 20: 3273.
https://doi.org/10.3390/w14203273