## Abstract

Water–air two-phase flow has been the theoretical basis of traditional building drainage systems. However, with the popularization of water saving devices, more research investigations need to be performed on the impact of solid waste on drainage systems. Through experiments under the solid waste scenario, the effects of drainage volume, diameter, and slope of the pipeline on the hydraulic performances of the horizontal main drain were investigated. The results showed that the drainage volume, diameter, and slope of the pipeline did not affect the location of the hydraulic jump on the horizontal main drain. The heights of the hydraulic jump were proportional to the discharge volumes and diameters of the pipeline, but inversely proportional to the slopes of the pipeline. The depth ratio was mainly responsible for the change of positive pressure value in the horizontal main drain. The depth ratios were proportional to the drainage volumes and inversely proportional to the diameters and slopes of the pipeline. The final deposition distances of solid wastes in the horizontal main drain were proportional to the discharge volumes and the pipeline slopes. The self-cleaning lengths of the clear water were 1.2∼1.6 times of the real final deposition distances of solid wastes.

## HIGHLIGHTS

The change of depth ratio caused the variation of positive pressure in horizontal main drain.

The location of hydraulic jump was not affected by the drainage volume, the diameter or the slope.

The height of the hydraulic jump was affected by the drainage volume, the diameter and the slope.

The depth ratio was affected by the drainage volume, the diameter and the slope.

The final deposition distance of solid wastes was affected by the drainage volume, the diameter and the slope.

## INTRODUCTION

As an essential component of the building drainage system, the horizontal main drain is responsible for discharging wastewater, including solid waste out of buildings. With the prevalence of water-saving toilets, the reduction of a single flush volume has led to a corresponding decrease in the drainage in the horizontal main drain. For this reason, the probabilities of solid waste deposition and air pressure fluctuations increased (Campbell 2018; Guan *et al.* 2022a, 2022b). Therefore, clarifying the factors affecting the hydraulic performance of building drainage horizontal main pipes plays an important role in deeply understanding the drainage system and maintaining its normal operation, and can effectively relieve the operating pressure of urban drainage systems (Eulogi *et al.* 2022).

The hydraulic performance of the horizontal main drain is influenced by many factors including the characteristics of a hydraulic jump, air pressure, water flow rate, and solid transport distance. Relevant studies have been reported in recent years. By mathematical deduction, Chen *et al.* (2003) studied the energy consumption of a hydraulic jump in an inclined circular pipe and thus proposed a model for calculating the energy consumption coefficient of a hydraulic jump. By investigating the water flow in the DN100 horizontal pipe under the 6-L toilet, Oengoeren & Meier (2007) found solid waste deposition at 0.5 m from the sanitaryware outlet where the maximum depth ratio is less than 0.25. Thus, he proposed that it was difficult to transport solids at low water levels. By comparing the solid waste transport performances in the pipes with non-circular sections, Cummings *et al.* (2007) found that the transport capacity for solid waste could be enhanced by increasing the water depth under low flush conditions. This was because of larger buoyancy at higher water depths. The results by McDougall & Wakelin (2007) also showed that transportation efficiency in the low discharge volume would be improved by reducing the cross-sectional area of the pipeline and increasing the water depth in the pipe. The smaller the cross-section the stronger the continuous impact capacity of water flow. The deeper the water flow, the smaller the friction between the water flow and the pipe wall. Otsuka (2015) found that no deposition occurred in the horizontal pipe when the diameter of the solid did not exceed 70% of the water depth and the flow rate was not less than 0.6 m/s. DeMarco *et al.* (2013) investigated the effects of different discharge volumes, types of solid, and other factors on the solid waste transport performance in DN100 pipe under the instantaneous flow of water-saving toilets. They found that the type of toilet had little effect on the solid's transport performance. The discharge volume and the slope of the pipe were the main factors affecting the solids transport performance. In addition, Wu & Zhang (2014) studied the influence of two drainage methods on the water seal of appliances in horizontal branch pipes. They found that the water seal loss was equal to or close to 1/2 negative pressure value in the constant flow. However, the corresponding relationship was unclear between water seal loss and negative pressure value due to the large change of peak flow in instantaneous flow conditions. Its loss value was far less than that under constant flow conditions.

According to the existing research, it could be found that relatively fewer studies on the horizontal main drain compared with that of the drainage stack. There is no systematic view and understanding of the hydraulic characteristics of the horizontal main drain. The hydraulic jump is caused by the rapid change of the flow at the beginning of the main drain. It has an important impact on the water depth and the water fullness in the pipe, which in turn impedes the airflow in the pipe and thus leads to an increase of the positive pressure at the horizontal main drain (Najafzadeh 2019; Guan *et al.* 2022a, 2022b). However, the previous research focused on the energy change by hydraulic jump and the pressure fluctuation under the liquid–air two-phase constant flow. There have been relatively few studies on the impact of solids on hydraulic performance. The research on solid deposition performance was mostly carried out by theoretical derivation. The authenticity of solid deposition distance needs to be investigated by experimental research. In addition, most of the existing studies were conducted from a single perspective such as air pressure, transport performance, hydraulic jump, or depth ratio. There was a lack of comprehensive studies on the hydraulic performance of horizontal main drains. Therefore, in this study, an experimental drainage device was set up using the same proportion as the real system. By experiment, aspects including the characteristics of a hydraulic jump, air pressure, flow rate, and solid deposition distance of the horizontal main drain were researched in the building drainage system with solid waste. The main influencing factors included pipe diameter, drainage volume, and pipe slope. There were two types of diameter pipes, De110 and De90; and there were three types of drainage volumes, 6.0, 4.5, and 3.0 L. Three types of pipe slopes were also used in the experiment 0.012, 0.008, and 0.004. The results were significant to understand the actual drainage system deeply. The results also provided a reliable reference value for actual engineering design.

## MATERIALS AND METHODS

### Experimental device

*Standard for testing the drainage capacity of risers in building drainage systems*, CJJ/T 245-2016. A four-story (12.6 m) high single-stack drainage experimental device was built in the Beijing University of Civil Engineering and Architecture (BUCEA) laboratory, as shown in Figure 1. The proportion of the device was the same as the real system.

As shown in Figure 1, the drainage test device consisted of a drainage piping system and its control system. The drainage piping system had four floors with a total height of 12.6 m. The first floor was 3.2 m high. The second to fourth floors were 3.6 m high. The length of the horizontal drainage branch of each floor was 0.7 m. Its slope was 0.012. The branch was connected to the vertical pipe by TY-shaped three-way fittings. A siphon toilet was installed at the end of the branch on the third and fourth floors. The branch on the first and second floors was sealed with a casing cap. The horizontal main drain was 22.0 m long and was connected to the vertical pipe by two 45° elbows. The inflfluent and efflfluent of the toilet were controlled by PLC. The PLC control cabinet was a programmable control cabinet, which could realize the control of motors and switches. A liquid level sensor was set in the toilet tank controlling the water volume. A solenoid valve was used to control the drainage.

### Materials

#### Solid simulants

#### Polypropylene balls

### Methods

#### Test program

Four artificial test bodies were put into the drainage system as a group while the toilet on the third floor started to flush at the same time. The effect of pipe diameter, drainage volume, and pipe slope on four elements of hydraulic performance was investigated. Two pipe diameters (De110 and De90), three toilet drainage (3.0, 4.5, and 6.0 L), and three pipe slopes (0.012, 0.008, and 0.004) were used in this experiment. The four elements of hydraulic performance investigated were hydraulic jump, air pressure, water velocity, and solid waste transport distance. The specific experimental conditions of the test were set as shown in Table 1.

Control groups . | Diameter (mm) . | Flash volume (L) . | Slope . |
---|---|---|---|

1 | De110 | 6.0 | 0.012 |

2 | 4.5 | 0.012 | |

3 | 0.008 | ||

4 | 0.004 | ||

5 | 3.0 | 0.012 | |

6 | De90 | 6.0 | 0.012 |

7 | 4.5 | 0.012 | |

8 | 0.008 | ||

9 | 0.004 | ||

10 | 3.0 | 0.012 |

Control groups . | Diameter (mm) . | Flash volume (L) . | Slope . |
---|---|---|---|

1 | De110 | 6.0 | 0.012 |

2 | 4.5 | 0.012 | |

3 | 0.008 | ||

4 | 0.004 | ||

5 | 3.0 | 0.012 | |

6 | De90 | 6.0 | 0.012 |

7 | 4.5 | 0.012 | |

8 | 0.008 | ||

9 | 0.004 | ||

10 | 3.0 | 0.012 |

#### Test method

##### Hydraulic jump height and fullness degree test

First, an 80-cm-long horizontal steel ruler was set on the outer wall of the main drain along the flow direction. Second, starting from 20 cm from the center of the vertical pipe, a vertical direction steel ruler was set every 10 cm for a total of seven measurement points on the main drain. During the test, a high-speed camera was used to shoot the process of the hydraulic jump. After the test, the video was imported into the computer. Kinovea software was then used to play frame by frame to capture the water level height data. The values of hydraulic jump height and fullness degree were obtained.

##### Air pressure fluctuation test

##### Water velocity test

*et al.*(2016) discussing the Lagrangian particle-based computational fluid dynamics method, the peak flow velocity at a certain section in the main drain could be maintained for about 3 s, and then the flow velocity would drop rapidly. Thus, during the test, if the ball passed the section within 3 s, the value was valid. Otherwise, the test was repeated.

The velocity of both the polypropylene ball and the water flow at a certain section was obtained by dividing the distance of the polypropylene ball at each frame by the time interval. Since the degree of siphoning varied at each flush, thus the velocity values obtained were different. Therefore, the test was repeated three times at each section with the same flush volume. The average value of the velocities obtained from the three tests was taken as the final data.

##### Solid transport distance test

## RESULTS AND DISCUSSION

### Hydraulic jump characteristics

In Figure 8, under the test conditions and with the distance increasing, the water level heights and the fullness degrees on the horizontal main drain all rose at the beginning and then decreased. The peak values were located 30 cm from the center of the vertical pipe, indicating that the change in pipe diameter and the drainage volume did not affect the location of the hydraulic jump on the main drain at a fixed slope.

The peak values both of water level and fullness degree in De110 and De90 pipe diameters decreased by 7.7 and 15.5%, 2.4 and 7.2%, respectively, while the discharge volume decreased from 6.0 to 4.5 and 3.0 L. This indicated that both the peak values both of water level and fullness degree in the horizontal main drain increased with the increased discharge volume.

By comparing with the values under the De110 diameter, when water volume was 6.0, 4.5, and 3.0 L, the peak values of water level under the De90 diameter decreased by 12.9, 7.9, and 4.4%. However, the corresponding fullness degrees increased by 3.6, 9.6, and 13.9%. This meant that reducing the pipe diameter reduced the water level height but increased the fullness degree at the same time under the same water volume.

In Figure 9, similarly to Figure 8, under the test conditions and with the increase of distance from the center of the vertical pipe, the heights of the water level and the fullness degrees under each condition increased at the beginning and then decreased. The peak values all appeared at 30 cm indicating that the change of the pipe slope in the horizontal main drain did not affect the location of the hydraulic jump. When the slope was the same, the peak values of the fullness degree at the De90 pipe diameter were 9.6–12.2% higher than that at the De110 pipe diameter, which indicated that reducing the pipe diameter led to a higher fullness degree. The result was consistent with the result in Figure 8.

When the pipe diameter was fixed, the water level height and fullness degree were all slightly reduced with the increasing slope at the leap and its post-leap sections of hydraulic jump in the horizontal main drain. For example, under De110 and De90 pipe diameter, the peak values of water level and fullness degree decreased by 0.3 and 0.7% and 0.5 and 2.9%, respectively, while the slope increased from 0.004 to 0.008 and 0.012.

Under the pipe diameter De110, the slope is 0.004, 0.008, 0.012, the peak water level and its filling degree at 40 cm from the beginning of the cross-pipe, compared with 30 cm from the beginning of the cross-pipe attenuation of 0.3, 1.9, 8.3%, respectively. However, the attenuation in the same case was 7.7, 4.7, and 8.0%, respectively, at pipe diameter De90. It indicated that in a larger diameter pipe, the smaller the slope, the weaker the energy dissipation of the hydraulic jump, and the longer duration of the hydraulic jump.

*Z*

_{1}and

*Z*

_{2}are for the potential head at before-leap and after-leap sections. The difference between

*Z*

_{1}and

*Z*

_{2}was mainly caused by the difference in slope in the horizontal main drain. The greater the slope the bigger the difference.

*h*

_{1},

*h*

_{2}indicated the pressure head at before-leap and after-leap sections. Because the drainage system belongs to gravity flow, the values were equal to the heights of the water level of the two sections.

*V*

_{1}

^{2}/2 g and

*V*

_{2}

^{2}/2 g were velocity heads at before-leap and after-leap sections. △

*H*was the head loss between the two sections, which mainly consisted of the local head loss caused by hydraulic jump and frictional head loss by the pipe.

Almost all potential energy was converted into kinetic energy when water flowed from the vertical pipe into the horizontal main drain. Rapid flow appeared there. At the end of the rapid flow section, the flow velocity decreased due to the resistance of the pipe wall, and the water level rose to form a hydraulic jump. The research results of Chen Yame *et al.* showed that the head loss of a hydraulic jump was related to the height of the water jump, the slope of the main drain, the diameter of the main drain, and the cross-sectional area at the hydraulic jump (Smith & Chen 1989).

The test results in this section also showed that the discharge volume, slope, and pipe diameter had effects on the water level height and its decay rate. These changes also ultimately affected the flow velocity and solids transport performance through Equation (1), which would be discussed in Sections 3.3 and 3.4. In addition, the degree of fullness was an indicator to characterize the state of water filling in the pipe section. The greater the filling degree, the smaller the proportion of gas in the pipe section and the larger the positive pressure value in the main drain, which would be verified by the air pressure test in Section 3.2.

### Air pressure fluctuation characteristics

In Figure 10, for De110 and De90 pipe diameters, the air pressure values at different locations on the horizontal main pipe decreased by 6.5–22.8% and 15.2–29.0%, 4.0–13.3%, and 9.73–21.8%, respectively, as the drainage volume was reduced from 6.0 to 4.5 and 3.0 L. It indicated that the reduction of the drainage volume, to a certain extent, alleviated the positive pressure value in the horizontal main drain. According to the experimental result in Section 3.1, the fullness degree decreased with the drainage volume decreasing. The result of Figure 10 was consistent with the result in Section 3.1. Wang (2014) studied the variation of positive pressure in the horizontal drainage pipe from 6 to 24 L under the clear water condition. The results are also consistent with this study, indicating that the value of the positive pressure in the transverse trunk pipe decreases with decreasing discharge volume for both the clear water condition and the discharged solids condition.

Compared with the pipe diameter at De110, the positive pressure values at De90 increased by 16.3–35.3%, 16.2–45.0%, and 16.9–56.0% for the three discharge volumes. This indicated that reducing the pipe diameter generated higher positive pressures, which was also consistent with the result of the fullness test in Section 3.1.

From Figure 11, under De110 and De90 pipe diameters, positive pressure values at various points in the main drain increased by 38.4–47.8% and 45.31–82.1%, 20.7–32.5%, and 33.65–61.34%, respectively, as the slopes were reduced from 0.012 to 0.008 and 0.004. This indicated that the decrease in pipe slope led to the positive pressure values increasing in the main drain. For the three slopes, the positive pressure values at different points in the De90 pipe diameter cross trunk pipe increased by 25.6–45.0%, 12.4–35.3%, and 15.0–34.7% compared to the De110 pipe diameter. The above results were consistent with the results of the fullness test in Section 3.1.

In summary, the air pressure test results under each condition in this section were consistent with the test results of the filling degree in Section 3.1. The larger the fullness degree, the larger the positive pressure value in the main drain. It could be concluded that the drainage volume, pipe diameter, and pipe slope all affected the flow resistance of the gas in the pipe by affecting the fullness degree, and ultimately leading to the change of the air pressure value in the main drain.

### Water flow velocity characteristics

The initial movement velocity of the deposited solids in the horizontal main drain was caused by the impact force of the water flow from the next flush. Hence the clear water flow rate was commonly used as an worldwide important basis for determining the solids transport performance of horizontal main drains.

From Figures 12 and 13, it could be found that the actual flow velocity displayed a fluctuating decreasing trend along the horizontal main drain. The fitting data results showed that the correlation coefficients for each condition were greater than 0.95. This indicated that the fitted curves well reflected the variation pattern of the measured data. Walski *et al.* (2011) calculated the flow velocity in the horizontal pipe using the Manning Equation and compared it with the solid transport situation based on the flow, slope, and roughness test data. The study concluded that 0.6 m/s was the threshold flow rate for solids transport. Based on the above results, the self-clearing distance was defined in this study, which is a section of the pipe length from the center of the vertical pipe to the section with a flow velocity equal to 0.6 m/s. The solid simulant transport performance in the main drain was discussed from the flow velocity perspective.

According to Figure 12, for De110 and De90 pipe diameters, as the discharge volume decreased by 4.5 and 3.0 L from 6.0 L, the corresponding maximum flow velocities decreased by 20.3 and 33.5%, 16.8 and 39.5%, respectively. At the same time, the self-cleaning distances decreased by 32.0 and 50.7%, 25.0, and 43.2%, respectively. This indicated that both the flow rate and self-cleaning distance increased as the discharge volume increased. Compared with the pipe diameter at De90, the initial flow rate at De110 was greater. However, due to the faster decay at De110, the flow velocity was overtaken by De90 in the later stage. Therefore, the self-cleaning distance at De110 was also relatively small. Under drainage volume 6.0 L, the self-cleaning distances at De110 and De90 were the same. However, the self-cleaning distance increased by 10.3 and 15.3%, respectively, when the drainage volume reduced from 6.0 to 4.5 and 3.0 L. This showed that it was helpful for solid transportation if the smaller pipe diameter matched the lower drainage volume.

In Figure 13, for De110 and De90 pipe diameters, as the slope was reduced from 0.012 to 0.008 and 0.004, respectively, the corresponding self-cleaning distance decreased by 4.2 and 15.1%, 30.1 and 40.3%. The larger the slope was, the larger the self-cleaning distance was when the pipe diameter and discharge volume were fixed. Compared with the pipe diameter at De110, the self-cleaning distance at De90 increased by 10.3% when the slope was 0.012. However, the self-clearing distances at De90 were reduced by 19.5 and 22.4% when the slope was reduced from 0.012 to 0.008 and 0.004. Indicating it was helpful for solid transport if a smaller pipe diameter matched with a larger slope.

*V*was the solid moving speed,

_{s}*L*was the solid moving distance in the horizontal tube,

*G*was the slope of the horizontal pipe,

*C*

_{1}and

*C*

_{2}were constants. When the solid moving speed

*V*= 0, the solid stopped moving.

_{s}*L*was the final transport distance at this time. Thus, it can be seen that

*L*was positively correlated with the slope of the horizontal tube

*G*. The above conclusions were consistent with the experimental results of this study.

### Solid transport distance

In real building drainage systems, solids were the main cause of clogging (Gormley *et al.* 2021). Therefore, although the flow velocity distribution law in the main drain could reflect the transport capacity of the main drain from the side, it was difficult to determine the actual solid transport distance. McDermott *et al.* (2019) found that ‘in the main drain of a drainage system, the velocity of solids movement depended mainly on the water flow conditions around the solids… the less the accompanying water volume was, the more likely deposition occurred’, meaning that there was a maximum transport distance for any fouling in the main drain. As the water flow moved toward the end of the main drain, the flow velocity gradually decreased. The distance that could push the solids to move also gradually decreased. Eventually, the solids deposited in the main drain and could not be pushed forward. This section continued to explore the effects of pipe diameter, discharge volume, and slope on the final transport distance in the horizontal main drain.

From Figure 14, for De110 and De90 pipe diameters, the final average deposition distances of solid simulants were 10.9 and 10.57 m when the drainage volume was 6 L. The distances were 9.95 and 10.13 m when the drainage volume was 4.5 L. The distances were 7.31 and 7.52 m when the drainage volume was 3 L. The above results indicated that the final solid deposition distances shortened with the decrease of drainage volume in the fixed pipe diameter. Compared with the pipe diameter at De110, the average final solid deposition distance at De90 decreased by 3.0% when the discharge volume was 6.0 L, while the values at De90 increased by 1.8 and 2.9% when the discharge volume was 4.5 and 3.0 L, respectively. The results were consistent with the test results on flow rate and self-cleaning distance in Section 3.3, indicating that smaller pipe diameters matched with lower discharge volume helped in enhancing solid transport to some extent. Combining the results in Section 3.3, the deposition distance judged by flow velocity alone was 28.4 and 23.2% smaller than the actual deposition distance for the final deposition at De110 at De90.

For De110 and De90 pipe diameters, the final average solid settling distances were reduced by 8.7 and 32.9%, 4.2 and 28.9%, respectively, as the discharge volume was decreased from 6.0 to 4.5 and 3.0 L. Compared to the 6.0 L, it could be found that the transport performance of solids was significantly reduced for 3.0 L, but the reduction in transport performance was minor for 4.5 L. The results were in general agreement with the findings of the Plumbing Efficiency Research Coalition (PERC). The solid transport capacity of 4.5 L at DN100 pipe diameter was comparable to the 6.0 L. However, the transport capacity of 3.0 L was poor. It had too little water to maintain the push solids movement (DeMarco *et al.* 2013).

From Figure 15, under De110 and De90 pipe diameters, it was found that the final average solid deposition distance in the horizontal main drain was 9.95 and 10.13 m (*i* = 0.012), 8.05 and 7.08 m(i = 0.008), 7.47 and 6.36 m(i = 0.004), respectively. It indicated that the final solid deposition distance under the fixed pipe diameter was reduced with the decrease of the slope. The final deposition distance shortened with the reduction of the slope. Compared with the pipe diameter at De110, the average final deposition distance at De90 increased by 1.8% when the slope was 0.012, while the distances were reduced by 14.2 and 17.4%, respectively, when the slope was 0.008 and 0.004. It indicated that at the steep slope condition, reducing the pipe diameter was beneficial for enhancing the solid transport capacity. However, at the gentle slope, reducing the pipe diameter was harmful to solid transport. The results were consistent with the test results on flow rate and self-clearing distance in Section 3.3. It indicated that to enhance the solids transport capacity, smaller pipe diameters should be matched with steeper slopes. Combining the results of flow velocity and self-clearing distance in Section 3.3, the deposition distance judged by flow velocity alone was 29.3 and 31.2%, respectively, smaller than the actual deposition distance for the final deposition at De110 and De90.

Under the test conditions, when the slope was changed from 0.012 to 0.008, the slope was reduced by 33.3%, and the final average deposition distance was shortened by 30.1%. When the slope was changed from 0.008 to 0.004, the slope was reduced by 50%, and the final average deposition distance was shortened by only 10.2%. This was not entirely consistent with the conclusion of Otsuka *et al.* of Kanto Institute, Japan (Akiyama *et al.* 2015) which a 50% reduction in the slope of the pipe reduced its transport capacity by about 30%. According to the results of this study, although the solid transport capacity of the horizontal main drain was closely related to the slope value, the relationship between the solids transport capacity and the slope of the pipe was more likely to be exponential rather than linear.

## CONCLUSIONS

By building a single stack drainage system under the solid waste scenario, the effects of drainage volume, diameter and slope of the pipeline on hydraulic performances of the horizontal main drain were investigated. Hydraulic performances have four influencing factors including hydraulic jump, air pressure, water velocity and solid waste transport distance. The main conclusions were shown as follows.

- (1)
The location of the hydraulic jump on the horizontal main drain was not affected by the drainage volume, pipe diameter or pipe slope. Under the test conditions, the distance between the center of the vertical pipe and the peak height of the hydraulic jump was 30 cm.

- (2)
The height of the hydraulic jump in the main drain was proportional to the discharge volume and pipe diameter while inversely proportional to the slope. The fullness degree was proportional to the discharge volume while inversely proportional to the pipe diameter and pipe slope. Slope of 0.004 and 0.008 at De110 led to the extension of the peak duration of the hydraulic jump. Under the test conditions, the hydraulic jump height and maximum fullness degree were reduced by 7.2–15.5% as the discharge volume was reduced from 6.0 to 3.0 L. The hydraulic jump height and maximum fullness degree were increased by 0.4–2.9% when the slope was reduced from 0.012 to 0.004. When the pipe diameter changed from De110 to De90, the hydraulic jump height was reduced by 4.4–12.9%, and the maximum fullness degree was increased by 3.6–12.1%.

- (3)
Filling degree was the main reason for the variation of the positive pressure value in the horizontal main drain. Similar to the fullness degree, the positive pressure value was also proportional to the discharge volume while inversely proportional to the pipe diameter and pipe slope. By comparing the pipe diameter and discharge volume, the results showed that the slope had the most significant effect on the positive pressure value. Under the test condition, the maximum positive pressure value decreased by 14.8–15.2% while the discharge volume decreased from 6 to 3 L. The maximum positive pressure values increased by 33.7–45% when the slope decreased from 0.012 to 0.004. The maximum positive pressure values increased by 16.2–34.3% when the pipe diameter changed from De110 to De90.

- (4)
The final solid deposition distances in the horizontal main drain were proportional to the discharge volume and pipe slope. The effect of the slope was the most significant. Under the test conditions, the solid deposition distance increased up to 37.2% when the slope was increased from 0.004 to 0.012. The effect of pipe diameter on the flow velocity and final deposition distance should be considered in sections. For a discharge volume of 6 L and a slope of 0.012, a pipe diameter of De90 should be used to increase the flow rate and the final deposition distance. The pipe diameter of De110 could improve the flow rate and increase the deposition distance when the discharge volumes were 4.5 and 3.0 L, and the slopes were 0.008 and 0.004.

- (5)
The self-cleaning distance determined based on the self-cleaning flow rate under clear water conditions could be used to characterize the final solid deposition distance in the horizontal main drain. However, self-cleaning distances were smaller than real solid deposition distances and should be corrected by 1.2–1.6 times.

## ACKNOWLEDGEMENTS

This study was supported by the National Natural Science Foundation of China (No. 51578035) and the National Major Water Pollution and Treatment Project of China (No. 2018ZX07110-008-006). Thanks to Peihan Wu from Emory University for her valuable assistance with English translations and expressions of the manuscript.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

## REFERENCES

*Buildings*

**11**(2), 70.