Causes and consequences of changes in the values of hydraulic characteristics of metal water supply and sanitation networks during their operation

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Introduction

During their operation life cycle, water supply networks made of metal pipes (gray cast iron), as well as drainage networks made of any type of material, are subject to the formation of a layer of internal deposits on the pipe walls under certain conditions, which change the values of the characteristics of the hydraulic potential of the pipes (V, d_in, i) [1–6].

Figure 1 presents fragments of deposits on the inner surfaces of metal water supply and wastewater networks.

 

Fig. 1. Fragments of internal deposits on the walls of metal pipes. a,b – Pressure drainage networks; c,d – gravity drainage networks

 

A layer of internal deposits on the walls of pipes causes consequences that change the values of the characteristics of the hydraulic potential of pipes and affect the duration of use of worn-out networks and the energy consumption of pumping units for pressure networks and collectors [1, 2].

Table 2 lists the causes and consequences of changes in the hydraulic characteristics of water supply and wastewater pipelines with internal deposits.

 

Fig. 2. Causes and consequences of changes in the hydraulic characteristics of water supply and wastewater pipelines

 

Methods

Using a specific example (Fig. 1), we perform a hydraulic calculation and show changes in the values of the characteristics of the hydraulic potential of a pressure drainage collector made of cast iron pipes with a diameter d_n of 0.404 m.

Problem

A pressure cast iron collector with a diameter d_n of 0.404 m (GOST 9583-75) and a wall thickness S_p of 12.5 mm (0.0125 m) pumps wastewater flow q of 140 l/s (0.14 m³/s). The thickness of the layer of internal deposits σ is 25 mm (0.025 m).

We calculate and compare the values of the actual characteristics of the hydraulic potential of pipes $d_{\text{вн}}^{\text{ф}}$, $V_{\text{ф}}$, $i_{\text{ф}}$ and  and new cast iron pipes with a diameter  of 0.429 m. Here, we present the change in the energy consumption of the pumping unit $N_{\text{вн}}^{\text{ф}}$ for the given conditions of the problem.

Solution

1. Accounting for the actual internal diameter, we calculate the average flow velocity V_n for new cast iron pipes and pipes with a deposit layer thickness σ of 25 mm as follows:

$V_{\text{н}}=\frac{4·q}{\pi ·d_{\text{вн}}^{\text{2}}}=\frac{4·\mathrm{0,14}}{\mathrm{3,14}·{\mathrm{0,379}}^2}=\frac{\mathrm{0,56}}{\mathrm{0,4510}}=\mathrm{1,24}$ m/s;

$d_{\text{вн}}=d_{\text{н}}-2S_{\text{р}}=\mathrm{0,404}-\mathrm{0,025}=\mathrm{0,379}$ m;

$d_{\text{вн}}^{\text{ф}}=\left(d_{\text{н}}-2S_{\text{р}}\right)-2\sigma =\left(\mathrm{0,404}-\mathrm{0,025}\right)-2·\mathrm{0,025}=\mathrm{0,379}-\mathrm{0,05}=\mathrm{0,329}$ m;

$V_{\text{ф}}=\frac{4·\mathrm{0,14}}{\mathrm{3,14}·{\mathrm{0,329}}^2}=\frac{\mathrm{0,56}}{\mathrm{0,3399}}=\mathrm{1,65}$ m/s.

 

2. The values of the hydraulic slope are calculated for new cast iron pipes d_n and for pipes with a layer of deposits σ of 0.025 m. The calculation was made using the following equations [7, 8]:

$i_{\text{н}\left(\text{ф}\right)}=\mathrm{0,00107}\frac{V_{\text{н}\left(\text{ф}\right)}^{\text{2}}}{{\left[\left(d_{\text{н}}-2S_{\text{р}}\right)-2·\sigma \right]}^{\mathrm{1,3}}}$, m/m;

$i_{\text{н}}=\frac{\mathrm{0,00107}·{\mathrm{1,24}}^2}{{\left[\mathrm{0,404}-2·\mathrm{0,0125}\right]}^{\mathrm{1,3}}}=\frac{\mathrm{0,00165}}{{\mathrm{0,379}}^{\mathrm{1,3}}}=\frac{\mathrm{0,00165}}{\mathrm{0,2833}}=\mathrm{0,00582}$ m/m;

$i_{\text{ф}}=\frac{\mathrm{0,00107}·{\mathrm{1,65}}^2}{{\left[\left(\mathrm{0,404}-2·\mathrm{0,0125}\right)-2·\mathrm{0,025}\right]}^{\mathrm{1,3}}}=\frac{\mathrm{0,00291}}{{\mathrm{0,329}}^{\mathrm{1,3}}}=\frac{\mathrm{0,00291}}{\mathrm{0,2357}}=\mathrm{0,01234}$ m/m.

 

The changes in the actual values of the hydraulic characteristics of cast iron pipes d_in of 0.404 m with different thicknesses of the layer of internal deposits of 0 ÷ 30 mm (0 ÷ 0.03 m) are given in Table 1.

 

Table 1

Deposited layer thickness σ (m)	Actual average velocity Va (m/s)	Actual internal diameter of pipes with deposits  (m)	Actual specific pressure loss 1000 ia	Pipeline hydraulic efficiency coefficient
0	1.24	0.379	5.81	1.0
0.005	1.31	0.369	6.71	0.87
0.01	1.38	0.359	7.72	0.76
0.018	1.52	0.343	9.94	0.58
0.02	0.55	0.339	10.49	0.56
0.03	2.47	0.319	28.83	0.14

 

According to the authors, the operating efficiency of pressure and nonpressure water supply and wastewater pipelines (K^*_eff) should be assessed using the value of the dimensionless coefficient of the hydraulic efficiency of pipelines, which is the ratio of the energy consumption of pumping equipment installed in the new pipeline $N_{\text{дв}}^{\text{р}}$ to the value of energy consumption in the pipeline with the actual thickness of the deposit layer ${\sigma }_{\text{ф}}$ – $N_{\text{дв}}^{\text{ф}}$ or the ratio of the product of the values of the characteristics of the hydraulic potential of new pipes ( $V_{\text{p}}$, $d_{\text{дв}}^{\text{р}}$, and $i_{\text{p}}$) to the product of the values of the same characteristics for pipes with a specific thickness of the deposit layer σ_a on their inner surface [9]:

${\text{К}}_{\text{эф}}=\frac{N_{\text{дв}}^{\text{p}}}{N_{\text{дв}}^{\text{ф}}}=\frac{V_{\text{p}}\cdot \left(d_{\text{вн}}^{\text{р}}\right)\cdot i_{\text{р}}}{V_{\text{ф}}\cdot \left(d_{\text{вн}}^{\text{ф}}\right)\cdot i_{\text{ф}}},$, (1)

where $N_4^P$ is the rated value of the energy consumption of the pumping unit in the new pipeline (kW/h); $N_{\text{дв}}^{\text{ф}}$ is the actual value of energy consumption of a pumping unit operating in a pipeline with a deposit layer thickness σ_a (kW/h); $V_{\text{p}}$, $d_{\text{вн}}^{\text{р}}$, and $i_{\text{р}}$ are the values of the calculated (certified) characteristics of the hydraulic potential of new pipes at the time of putting the pipeline into operation; and $V_{\text{ф}}$, $d_{\text{вн}}^{\text{ф}}$, and $i_{\text{ф}}$ are the values of the actual characteristics of the hydraulic potential of worn pipes with deposits at the time of assessment.

The limiting value of the layer thickness of internal deposits σ in Table 1 is presented in bold.

The analysis of the values of hydraulic characteristics presented in Table 1 revealed the following.

For the conditions of the given example, the values of the actual internal diameter of a pipe with internal deposits of different thicknesses decreased from a d_in of 0.400 m (pipe without deposits) to a $d_{\text{вн}}^{\text{ф}}$ of 0.319 m (pipe with a layer of deposits σ = 0.03 m, i.e., by 15.83% or 1.19 times). This resulted in an increase in the flow speed from V = 1.24 m/s (in a new cast iron pipe) to V_a = 2.47 m/s (in a pipe with a deposited layer of σ = 0.03 m), that is, by 49.8% or 1.99 times.

Under these conditions, in comparison with a new pipe, the values of the actual pressure loss due to resistance along the length (hydraulic slope) i_a increased in the range i_p = 0.00581 m/m ≤ i_a ≤ 0.02883 m, that is, by 51.29% (pipe with a layer of deposits σ = 0.03 m) or by 4.96 times.

According to Table 1, a graph of the dependence $i_{\text{ф}}$ = f(σ) is plotted in Figure 3, confirming that the smaller the value of the actual internal diameter $d_{\text{вн}}^{\text{ф}}$ in pipes with a deposited layer σ, the greater the value of the hydraulic slope i_a and the greater the value of the actual flow velocity V_a. This was also confirmed by the values of the hydraulic efficiency coefficient of the pipeline K_eff, which, for the given example, characterized the influence of the layer thickness of internal deposits σ on the values of the pipeline hydraulic characteristics.

 

Fig. 3. Dependency graph i_a = f(σ)

 

For the given example, we determined the limit value of σ, above which further operation of the pipeline is unacceptable—0.018 m (Table 1). That is, at σ_a of 0.018 m, the pipeline must be decommissioned.

An expert assessment by specialists involved in the operation of water supply networks made of metal pipes recommends the following:

The decrease in the actual internal diameter of steel and cast iron pipes (made of gray cast iron) with internal deposits should not exceed 5% of the nominal internal diameter of the pipes; that is,

$d_{\text{вн}}^{\text{ф}}\le d_{\text{вн}}=\left(d_{\text{н}}-2·S_{\text{р}}\right)-2\sigma \le 5\%.$

For the example given, this corresponds to

 $d_{\text{вн}}^{\text{ф}}=d_{\text{вн}}^{\text{н}}-5\%=\mathrm{0,379}-\mathrm{0,01895}=\mathrm{0,360}$m.

Therefore, for the given example, the limiting value of the actual thickness of the deposit layer σ_a should not exceed the value

${\sigma }_{\text{ф}}$ = 0.379 − 0.360 = 0.018 m (1.8 mm).

This is indicated in bold in Table 1.

In this case, the limiting value of the pipeline hydraulic efficiency coefficient K_eff is as follows:

${\text{K}}_{\text{эф}}=\frac{\mathrm{0,00581}\cdot {\mathrm{0,379}}^2\cdot \mathrm{1,24}}{\mathrm{0,00994}\cdot {\mathrm{0,343}}^2\cdot \mathrm{1,52}}=\frac{\mathrm{0,001035}}{\mathrm{0,001778}}=\mathrm{0,58.}$

This proves that with a value K_eff of 0.58, further operation of the pressure manifold with a diameter d_n of 0.404 m is unacceptable.

For the conditions of the problem considered, we calculated the actual energy consumption of pumping equipment $N_{\text{дв}}^{\text{p}}$ installed on a pressure manifold with a diameter d_n of 0.404 m and an internal deposit layer thickness σ_a of 0.03 m (30 mm).

The methodology for calculating the energy consumption values of pumping and power equipment $N_{\text{дв}}^{\text{p}}$ has been presented in previous studies [2, 9].

The value of $N_{\text{дв}}^{\text{p}}$ for the conditions of the given example was calculated using the following equation [9, 10]:

$N_{\text{дв}}^{\text{p(ф)}}={10}^6\cdot i_{\text{р(ф)}}\cdot {\left(d_{\text{вн}}^{\text{p(ф)}}\right)}^2\cdot V_{\text{р(ф)}}\cdot \frac{\mathrm{0,00808}}{\eta }$, kW/h, (2)

where $N_{\text{дв}}^{\text{p(ф)}}$ is the value of energy consumption of pumping equipment in the new (p) and worn-out (a) pipelines at the time of assessment (kW/h); $i_{\text{р(ф)}}$, $d_{\text{вн}}^{\text{p(ф)}}$, and $V_{\text{р(ф)}}$ are the values of the characteristics of the hydraulic potential of new (р) and worn-out (a) pipes with a deposited layer thickness σ; and

About the authors

Oleg A. Prodous

INKO-Engineering LLC

Author for correspondence.
Email: pro@enco.su

doctor of engineering science, professor, ceo

Russian Federation, 190005, St. Petersburg, Moskovsky pr., 37/1, lit. Ah, pom. 1-N

Dmitry I. Shlychkov

Moscow State University of Civil Engineering

Email: ShlyichkovDI@mgsu.ru

phd in engineering science, associate professor of the water supply and wastewater chair, deputy director of the institute of engineering and environmental construction and mechanization

Russian Federation, 129337, Moscow, Yaroslavl sh., 26, ULB, office 322g

Petr P. Yakubchik

St. Petersburg State University of Railways of Emperor Alecsandr I

Email: P.Jakub@mail.ru

phd in engineering science, professor of the water supply and drainage and hydraulics chair

Russian Federation, 105187, St. Petersburg,Moskovsky pr., 9

References

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