CN107476507A - The suspention length of tube check method of siphonic drainage system - Google Patents
The suspention length of tube check method of siphonic drainage system Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E04—BUILDING
- E04D—ROOF COVERINGS; SKY-LIGHTS; GUTTERS; ROOF-WORKING TOOLS
- E04D13/00—Special arrangements or devices in connection with roof coverings; Protection against birds; Roof drainage ; Sky-lights
- E04D13/04—Roof drainage; Drainage fittings in flat roofs, balconies or the like
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Abstract
The invention discloses a kind of check method of siphon drainge system suspention length of tube, take actual siphon to start the time first and suspend the relational expression between length of tube in midair, designed displacement is calculated based on local meteorologic parameter condition and building structure parameter afterwards, starts the requirement of time to siphon based on the specifications of CECS183 2015 and the physical dimension of gutter calculates maximum siphon and starts the time；The first restrictive condition of suspention length of pipe is drawn not less than designed displacement by actual displacement；The second restrictive condition of suspention length of pipe is drawn no more than the maximum siphon startup time by the actual siphon startup time；Column pipe suitable length is drawn and to the siphon drainge system progress column pipe length check of design according to the first restrictive condition and the second restrictive condition.Whether the suspention length of tube that this method is used to verify design is reasonable, provides method of calibration before being come into operation for siphon drainge system so that the actual motion effect of siphon drainge system is preferable.
Description
Technical Field
The invention relates to the technical field of siphon drainage, in particular to a method for checking the length of a suspension pipe of a siphon drainage system.
Background
Compared with the traditional drainage system, the siphon rainwater drainage system has the advantages of large drainage quantity, rapid drainage, no gradient of the horizontal hanging pipe, space saving and the like, and is widely applied to certain buildings with large span and large volume, such as airports, convention and exhibition centers, stadiums and the like.
The existing siphon rainwater drainage system usually designs the length of the hanging pipe to be longer in consideration of the following factors. The factor one is that the building span is large; factor two, the hanger tube may be slotless; and by the factor of three, the increase of the length of the suspension pipe can reduce the number of the vertical drainage pipes, so that the engineering has the effects of obviously saving materials and reducing the cost. There are problems with increasing hanger length without throttling, which can result in increased system on-way resistance, reduced system maximum displacement, increased siphon start-up time, and the risk of gutter overflow as hanger length increases. It follows that a reasonable length of the hanger tube may promote better operation of the drainage system.
Because the prior art lacks the research of the influence of the length of the suspension pipe on the siphon drainage system, the siphon drainage system cannot well determine a reasonable length value of the suspension pipe during design, and an effective suspension pipe length checking method is not available before the system is put into use, so that the actual operation effect of the siphon drainage system is unsatisfactory. Therefore, there is a need for a method for checking the length of the suspension pipe of the siphon drainage system.
Disclosure of Invention
The invention mainly aims to provide a method for checking the length of a suspension pipe of a siphon drainage system, so as to solve the problem of siphon drainage in the prior art.
In order to achieve the above object, the present invention provides a method for checking the length of a suspension pipe of a siphon drainage system.
The invention discloses a method for checking the length of a suspension pipe of a siphon drainage system
(1) Obtaining a relational expression between actual water discharge and the length of the suspension pipe by a maximum water discharge calculation method according to the length and the diameter of a pipeline of the designed siphon water discharge system and obtaining a relational expression between actual siphon starting time and the length of the suspension pipe by a siphon starting time calculation method;
(2) Calculating the designed water discharge based on the local meteorological parameter conditions and the house structure parameters;
(3) Calculating the maximum siphon starting time based on the requirements of CECS183-2015 specifications on siphon starting time and the structural size of the gutter;
(4) Obtaining a first limiting condition of the length of the suspension water pipe through the actual water displacement not less than the designed water displacement;
(5) Obtaining a second limiting condition of the length of the suspension water pipe according to the fact that the actual siphon starting time is not more than the maximum siphon starting time;
(6) And obtaining the proper length of the suspension pipe according to the first limiting condition and the second limiting condition, and checking the length of the suspension pipe for the designed siphon drainage system.
The method can be used for verifying whether the length of the designed suspension pipe is reasonable or not, and provides a verification method before the siphon drainage system is put into use, so that the actual operation effect of the siphon drainage system is better.
Further, the maximum water discharge calculation method includes the steps of
Obtaining a nonlinear equation of actual flow and the length of the hanging pipe through a Bernoulli equation according to known parameters of the length of a tail pipe, the length of a vertical pipe, the diameter of the tail pipe, the diameter of the hanging pipe and the diameter of the vertical pipe of a siphon drainage system pipeline;
and selecting different lengths of the suspension pipe to obtain different actual flows, and then linearizing the nonlinear equation by using a Newton iteration method to obtain a linear equation of the actual flows and the lengths of the suspension pipes.
Further, when the diameter of the system pipeline is always consistent, the nonlinear equation of the actual flow and the length of the suspension pipe is
Where Q is the actual flow, d j Is the diameter of the system pipeline, xi is the local resistance coefficient, k is the absolute equivalent roughness, Z 1 Is the height from the top surface of the siphon drainage system to the end surface of the water outlet.
Further, the step of obtaining the nonlinear equation of the actual flow rate and the length of the suspension pipe is as follows:
the flow rate of the system is determined according to the difference between the power and the resistance of the Bernoulli equation
Wherein, Z 1 Is the distance from the top surface of the tail pipe to the bottom surface of the riser, h 1-2 Is the loss of resistance to flow of the fluid in the pipe through the top surface of the liner to the bottom surface of the riser:
h 1-2 ＝h f +h m
the on-way resistance calculation formula adopts the following formula:
h f ＝∑RL
in the formula:
h f -loss of on-way resistance (mH 2O);
r-hydraulic ramp down (mH 2O);
l-pipe length (m);
λ -coefficient of on-way drag;
d j -the calculated diameter (m) of the pipe;
Re-Reynolds number;
k-absolute equivalent roughness (mm);
l-pipe length (m);
γ -viscosity of water (m 2/s);
the local resistance calculation formula is as follows:
in the formula:
h m -local drag loss (mH 2O);
xi-local resistance coefficient;
v is the flow velocity (m/s) at a certain section of the pipeline.
Further, when the pipeline of the system is variable in diameter, the relation of the flow velocity of each section is found through a continuity equation, and the local resistance and the on-way resistance are calculated in a subsection mode to obtain a nonlinear equation of the maximum flow of the system and the length of the suspension pipe.
Further, the newton iteration method is as follows: let f (Q) =0, newton's method iteration formula be:
using mathematical software programming to perform iterative calculations, specifying conditions for stopping iteration, e.g. Q k-1 -Q k Theta is an allowable error, when the condition is met, the calculation is stopped, and Q is considered k-1 Is the maximum displacement Q of the siphon drainage system.
Further, the siphon start time calculation method comprises the following steps
Defining a boundary of an upstream pipeline and a downstream pipeline in a siphon drainage system;
obtaining the volume of an upstream pipeline of the siphon drainage system according to known parameters, namely the length of a tail pipe, the upstream length of a vertical pipe, the diameter of the tail pipe, the diameter of a suspension pipe and the diameter of the vertical pipe of the siphon drainage system;
determining a relational expression between the upstream pipeline filling time and the actual flow according to the volume of the upstream pipeline;
defining a correction relational expression of siphon starting time and upstream pipeline filling time, and substituting the relational expression of the upstream pipeline filling time and actual flow into the correction relational expression;
and selecting different lengths of the suspension pipe to obtain different actual flows, obtaining a correction coefficient in a correction relation, and finally obtaining a linear equation of the siphon starting time and the suspension pipe.
Further, the upstream pipe filling time and the actual flow rate are related by
Wherein
The correction relation between the siphon start time and the upstream pipeline filling time is T C ＝αT C +β
Wherein, T C Upstream pipe fill time, V upstream pipe volume, Q actual flow, V 1 Volume of tail pipe, V 2 Is the volume of the suspension pipe, V 3 Is the volume of the stand pipe, d 1 Diameter of tail pipe, d 2 Diameter of the suspension pipe, d 3 Is the diameter of the stand pipe; l is 1 Is the length of tail pipe, L 2 To the length of the suspension tube, L 3 Both α and β are correction factors for riser length.
Further, the design water discharge is calculated and obtained according to the years of the rainstorm reappearing period, the actual rainstorm intensity, the rainfall duration and the catchment area as known parameters.
Further, the CECS183-2015 specification in step (3) specifies that the siphon start time should not exceed 60s and the effective water storage volume of the gutter should not be less than the rainfall amount of the start time;
if the time is more than 60s or the slope of the roof is more than 2.5 percent and the gutter is full of water and overflows into the room, the effective water storage volume of the gutter should not be less than the designed rainwater flow of the catchment area for 2min and should not be less than the rainfall of the siphon start time.
Therefore, the method can be used for verifying whether the length of the designed suspension pipe is reasonable or not, and provides a verification method before the siphon drainage system is put into use, so that the actual operation effect of the siphon drainage system is better. The invention is suitable for the technical field of siphon drainage systems.
The invention is further described with reference to the following figures and detailed description. Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
FIG. 1 is a schematic diagram of a siphonic drainage system.
FIG. 2 is a graph showing the relationship between the maximum siphon flow and the length of the suspension pipe in theoretical calculation
Fig. 3 is a graph of the effective water storage height of the gutter and the length of the suspension pipe.
Detailed Description
The invention will be described more fully hereinafter with reference to the accompanying drawings. Those skilled in the art will be able to implement the invention based on these teachings. Before describing the present invention in detail with reference to the accompanying drawings, it is to be noted that:
the technical solutions and features provided in the present invention in the respective sections including the following description may be combined with each other without conflict.
Furthermore, the embodiments of the invention described in the following description are generally only examples of a part of the invention, and not all embodiments. Therefore, all other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without any creative effort shall fall within the protection scope of the present invention.
With respect to terms and units in the present invention. The terms "comprising," "having," and any variations thereof in the description and claims of this invention and in the related section are intended to cover a non-exclusive inclusion.
The invention discloses a method for checking the length of a suspension pipe of a siphon drainage system, which comprises the following steps
(1) Obtaining a relational expression between actual water discharge and the length of the suspension pipe by a maximum water discharge calculation method according to the length and the diameter of a pipeline of the designed siphon water discharge system and obtaining a relational expression between actual siphon starting time and the length of the suspension pipe by a siphon starting time calculation method;
(2) Calculating the designed water discharge based on the local meteorological parameter conditions and the house structure parameters;
(3) Calculating the maximum siphon starting time based on the requirements of CECS183-2015 specifications on siphon starting time and the structural size of the gutter;
(4) Obtaining a first limiting condition of the length of the suspended water pipe through the actual water displacement not less than the designed water displacement;
(5) Obtaining a second limiting condition of the length of the suspension water pipe according to the fact that the actual siphon starting time is not more than the maximum siphon starting time;
(6) And obtaining the proper length of the suspension pipe according to the first limiting condition and the second limiting condition, and checking the length of the suspension pipe for the designed siphon drainage system.
The method can be used for verifying whether the length of the designed hanging pipe is reasonable or not, and provides a verification method before the siphon drainage system is put into use, so that the actual operation effect of the siphon drainage system is better.
The maximum displacement calculation method includes the steps of
Obtaining a nonlinear equation of actual flow and the length of the hanging pipe through a Bernoulli equation according to known parameters of the length of a tail pipe, the length of a vertical pipe, the diameter of the tail pipe, the diameter of the hanging pipe and the diameter of the vertical pipe of a siphon drainage system pipeline;
and selecting different lengths of the suspension pipe to obtain different actual flows, and then linearizing the nonlinear equation by using a Newton iteration method to obtain a linear equation of the actual flows and the lengths of the suspension pipes.
When the diameter of the system pipeline is always consistent, the nonlinear equation of the actual flow and the length of the suspension pipe is
Wherein Q is the actual flow, d j Is the diameter of the system pipeline, xi is the local resistance coefficient, k is the absolute equivalent roughness, Z 1 Is the height from the top surface of the siphon drainage system to the end surface of the water outlet.
The steps of obtaining the nonlinear equation of the actual flow and the length of the suspension pipe are as follows:
the flow rate of the system is determined according to the difference between the power and the resistance of the Bernoulli equation
Wherein, Z 1 Is the distance from the top surface of the tail pipe to the bottom surface of the riser, h 1-2 Is the loss of resistance to flow of the fluid in the pipe through the top surface of the liner to the bottom surface of the riser:
h 1-2 ＝h f +h m
the on-way resistance calculation formula adopts the following formula:
h f ＝∑RL
wherein the content of the first and second substances,
in the formula:
h f -loss of on-way resistance (mH 2O);
r-hydraulic ramp down (mH 2O);
l-pipe length (m);
λ -coefficient of on-way drag;
d j -the calculated diameter (m) of the pipe;
Re-Reynolds number;
k-absolute equivalent roughness (mm);
l-pipe length (m);
γ -viscosity of water (m 2/s);
the local resistance calculation formula is as follows:
in the formula:
h m -local resistance loss (mH 2O);
xi-local resistance coefficient;
v is the flow velocity (m/s) at a certain section of the pipeline.
When the pipeline of the system has variable diameter, the relation of the flow velocity of each section is found through a continuity equation, and the local resistance and the on-way resistance are calculated in a subsection mode to obtain a nonlinear equation of the maximum flow of the system and the length of the suspension pipe.
The newton iteration method is as follows: let f (Q) =0, newton's method iterative formula is:
using mathematical software programming to perform iterative calculations, specifying conditions for stopping iteration, e.g. Q k-1 -Q k Theta is allowable error, when the condition is satisfied, the calculation is stopped, and Q is considered k-1 Is the maximum displacement Q of the siphon drainage system.
The siphon start time calculation method comprises the following steps:
defining a boundary of an upstream pipeline and a downstream pipeline in a siphon drainage system;
obtaining the volume of an upstream pipeline of the siphon drainage system according to known parameters, namely the length of a tail pipe, the upstream length of a vertical pipe, the diameter of the tail pipe, the diameter of a suspension pipe and the diameter of the vertical pipe of the siphon drainage system;
determining a relational expression between the upstream pipeline filling time and the actual flow according to the volume of the upstream pipeline;
defining a correction relational expression of siphon starting time and upstream pipeline filling time, and substituting the relational expression of the upstream pipeline filling time and actual flow into the correction relational expression;
and selecting different lengths of the hanging pipe to obtain different actual flows, obtaining a correction coefficient in a correction relation, and finally obtaining a linear equation of siphon starting time and the hanging pipe.
The relation between the upstream pipeline filling time and the actual flow is
Wherein
The correction relation between the siphon start time and the upstream pipeline filling time is T C ＝αT C +β
Wherein, T C For upstream pipe fill time, V is upstream pipe volume, Q is actual flow, V 1 Volume of tail pipe, V 2 Is the volume of the suspension pipe, V 3 Is the volume of the stand pipe, d 1 Diameter of tail pipe, d 2 Is the diameter of the suspended pipe, d 3 Is the diameter of the stand pipe; l is 1 Is the length of tail pipe, L 2 For the length of the suspension tube, L 3 Both α and β are correction factors for riser length.
And calculating to obtain the designed water discharge according to the years of the rainstorm reappearing period, the actual rainstorm intensity, the rainfall duration and the catchment area as known parameters.
In the step (3), the CECS183-2015 specification stipulates that the siphon start time is not longer than 60s and the effective water storage volume of the gutter is not smaller than the rainfall amount of the start time;
if the time is more than 60s or the slope of the roof is more than 2.5 percent and the gutter is full of water and overflows into the room, the effective water storage volume of the gutter should not be less than the designed rainwater flow of the catchment area for 2min and should not be less than the rainfall of the siphon start time.
Taking the actual meteorological parameters of a place as an example, theoretical analysis and numerical simulation calculation are carried out on all structural parameters of the single-bucket siphon drainage system to obtain Q-L 2 、T-L 2 And (4) checking the reasonable value range of the length of the suspension pipe according to the relational expression, and performing engineering application analysis.
Tail pipe length L in the present embodiment 1 Is 1m, the length L of the suspension pipe 2 10.85m, riser length L 3 4.5m, an upstream pipe internal diameter of 57mm and a downstream pipe internal diameter of 81.4mm. The top surface of the tail pipe is a section 1, and the bottom surface of the stand pipe is a section 2.
As shown in fig. 1, the siphon drainage system of the present invention includes a drainage tank 6, a siphon hopper 4, a tail pipe 1, a hanger pipe 2, a stand pipe 3, a makeup tank 7, and a circulating water pump 5.
The relation between the actual flow and the length of the suspension pipe is determined.
In a siphon drainage system, as long as the water inflow is sufficient, the final flow state is a full pipe flow state which can reach the maximum discharge capacity, so that the maximum drainage capacity is a system state value and is irrelevant to the flow development process.
The bernoulli equation is an energy equation for an ideal incompressible constant flow, and after considering the pipe frictional resistance of the actual fluid and the local resistance of the pipe, the energy equation of the water surface of the gutter and any section in the pipe can be expressed as:
in the formula: z is a linear or branched member 1 、Z 2 -height (m) of section 1, section 2 from the riser outlet;
p 1 、p 2 -static pressure of section 1, section 2;
υ 1 、υ 2 -flow velocity (m/s) of section 1, section 2;
γ — volume weight of fluid, γ = ρ g;
the alpha-kinetic energy correction coefficient is determined by the uniformity of the flow velocity distribution on the cross section. The flow velocity distribution is uniform, and alpha =1; the flow velocity distribution is not uniform, and the larger the α value. In the turbulent flow of the pipe flow, α =1.05 to 1.1. In the actual engineering calculation, 1 is selected;
h 1-2 the loss of resistance from section 1 to section 2, including the on-way resistance and the local resistance, is analyzed in detail later;
in addition, in the pipeline, the relation between the flow speed and the section size can be obtained by using a unitary flow continuity equation of the incompressible fluid:
υ 1 A 1 ＝υ 2 A 2
in the formula: a. The 1 、A 2 -cross-sectional area of section 1, section 2;
since the planes of section 1 and section 2 are both open to the atmosphere, the static pressure P is 1 、P 2 Are all 0. Get upsilon according to the above formula 1 ＝υ 2 ×A 2 /A 1 In general A 1 ＞＞A 2 ，It is understood that the difference between the power and the resistance of the system determines the flow rate of the system.
The loss of resistance of the fluid in the pipe flowing through two sections is the sum of the on-way resistance and the local resistance:
h 1-2 ＝h f +h m
the on-way resistance calculation formula adopts the following formula:
h f ＝∑RL
the above formula is implicit calculation formula, the calculation process is complicated, and for simplifying calculation, swame and Jain are adopted [ The proposed display calculation formula:
in the formula: h is a total of f Loss of on-way resistance (mH) 2 O)；
R-Hydraulic slope (mH) 2 O)；
L-pipe length (m);
λ -coefficient of on-way drag;
d j -the calculated diameter (m) of the pipe;
Re-Reynolds number;
k is absolute equivalent roughness (mm), and 0.06 is calculated in the following process according to the manufacturer providing the PVC pipeline and the data of the literature data;
l-pipe length (m);
gamma-viscosity of water (m) 2 S, where in the formula, γ = 1.006X 10 at 20 DEG C -6 m 2 /s)。
The local resistance calculation formula is as follows:
in the formula: h is m -local resistance loss (mH 2O);
xi-local resistance coefficient;
v is the flow velocity (m/s) at a certain x section of the pipeline;
q is the maximum displacement.
The local resistance coefficients of the various components in the system should be obtained by factory experiments, and when relevant data is lacked, the local resistance coefficients of the various components can be selected as shown in table 1 according to the display in the specification, but in practical application, the local resistance coefficients should be corrected according to data such as monitored pipeline pressure and the like.
The values of the local resistance coefficients of the water pipe assembly are shown in Table 1
TABLE 1
The height of a building is determined, the power of the siphon system is determined, and the analysis shows that the length of the suspension pipe can influence the on-way resistance of the pipeline, and further influence the maximum discharge capacity of the system. If the pipe diameters of the system are always consistent, the maximum flow Q of the system and the length L of the suspension pipe can be obtained by utilizing the upper application 2 The relational expression (c) of (c). Calculating the maximum displacement, if the diameter of the system is changed, finding the relation of the flow velocity of each section through a continuity equation, and calculating the local resistance h by sections m On-way resistance h i Obtaining the maximum flow Q of the system and the length L of the suspension pipe 2 The relational expression (c) of (a).
But Q-L is calculated no matter whether the pipe diameter is changed or not 2 The relational expressions are all nonlinear equations, in order to solve the complex equation, a Newton iteration method is adopted to linearize the nonlinear equation, the solution of the linear equation is gradually iterated to approximate the solution of the nonlinear equation, and f (Q) =0, wherein the Newton iteration formula is as follows:
programming with mathematical calculation software, performing iterative calculation, and stoppingConditions for stopping iteration, e.g. Q K-1 -Q K &Theta and theta are allowable errors, the calculation is stopped when the condition is met, and Q is considered K-1 Is the maximum displacement Q of the siphon drainage system. Inputting different lengths L of the suspension pipe 2 And Q values corresponding to different lengths of the suspension pipe can be obtained. By using the calculation results, the Q-L which is simpler and more convenient and is suitable for engineering is obtained by fitting 2 And (4) a relational expression.
Substituting the structural parameters of each part of the system into the formula
Iterative solution of different L by Newton iteration method 2 Setting an iteration stop condition according to the lower corresponding Q, wherein the allowable error theta =10 -6 Using MATLAB software to make programming calculation to change length L of suspended pipe 2 (5-150 m), and the Q value is calculated as shown in FIG. 2.
And then, selecting proper mathematical software to perform formula fitting by using the calculation result to obtain a relational expression between the maximum siphon discharge capacity and the length of the suspension pipe.
In the formula: q is the maximum water discharge of the system, L/s;
L 2 length of suspension pipe, L 2 ∈[5～150]m。
The fitting degree is judged by using the sum of squared errors SSE and a determination coefficient R-square, wherein SSE is the sum of squared errors of corresponding points of fitting data and original data, the closer to 0, the better the model fitting is shown, R-square is the ratio of SSR and SST, SSR is the sum of squares of differences between predicted data and the mean value of the original data, SST is the sum of squares of differences between the original data and the mean value, and the closer to 1, the better the interpretation capability of variables of the equation on y is shown.
Through calculation, the Sum of Squared Errors (SSE) =0.0089 and the determination coefficient (R-square) =0.9999 of the relational expression of the maximum siphon displacement and the length of the suspension pipe, the fitting degree is high in the independent variable interval range, a plurality of values of the suspension pipe in an interval of 5-100 m are selected from table 2, and the difference between the fitting formula and theoretical iterative calculation is compared. Q-L 2 The calculation result pairs are shown in table 2.
TABLE 2
As shown in Table 2, the fitting formula and the theoretical iterative calculation result have relative errors within +/-1%, and the relationship between the maximum flow of the siphon drainage system and the length of the suspension pipe can be well explained by using the fitting formula.
And then obtaining a relational expression between the actual siphon starting time and the length of the suspension pipe.
If the development of siphon drainage is regarded as an ideal process, assuming that the volume of an upstream pipeline of the system is filled with a small flow rate firstly, when water flow develops to the boundary position of the upstream pipeline and the downstream pipeline, the system immediately reaches the maximum siphon flow rate, when the liquid level of a gutter is reduced to a certain height, the system recovers the small flow rate to refill the system,
defining an upstream and downstream boundary of a siphon drainage system pipeline: if the suspension pipe and the stand pipe have no reducing diameter, the position 1m below the elbow at the tail end of the suspension pipe is used as the boundary between the upstream and the downstream of the siphon drainage pipeline system, if the reducing diameter exists, the position 10 times of the pipe diameter of the stand pipe at the downstream of the reducing diameter is used as the boundary, and because 4 factor changes which have large influence on siphon start-up time can bring about the change of the volume of the upstream pipeline, the research and analysis of simplified calculation of siphon start-up time by utilizing the volume of the upstream pipeline is suggested.
According to experimental tests and numerical simulation researches, the influence of the change of the volume of the upstream pipeline on the siphon starting time is large. According to the above assumptions, a filling time T is defined c ，T c In relation to system variables, is defined as the time at which the upstream pipe volume is filled at 60% of the maximum flow of the system. Suppose the volumes of a tail pipe, a hanger pipe and an upstream riser pipe in the volume of an upstream pipeline of a siphon drainage system are respectively V 1 、V 2 、V 3 . In addition, the maximum discharge flow Q of the system has been calculated in section 2.1, and 60% of the maximum flow is 0.6Q, the filling time T c This can be calculated by the formula:
selecting correction coefficients alpha and beta, and calculating the filling time T according to the numerical value c And (3) correcting, namely:
T＝αT c +β
changing the length of the suspension pipe, obtaining correction coefficients alpha and beta according to the numerical simulation result of siphon starting time, and further obtaining T-L 2 And (4) a relational expression.
The pipeline system of the siphon discharge experiment in fig. 1 was also used to perform the application analysis of the method. Calculating the volume V of the upstream pipeline according to the structural parameters of the pipeline system, and based on the obtained Q-L 2 FittingCalculating the corresponding 0.6Q under different lengths of the suspension pipe by a formula, and obtaining the filling time T c 。
In order to obtain the values of the correction coefficients alpha and beta, a calculation model of the single bucket siphon drainage system with different lengths of the suspension pipes is established for numerical simulation, the inlet flow is also set to be 20L/s, and the other settings are the same as those in section 4.2. Monitoring the cross section flow of the tail end pipeline of the suspension pipe, wherein the physical time when the cross section flow reaches 0.6Q is the siphon starting time T, T c The result of the calculation of sum T is shown as T in Table 3 c Theoretical calculation of sum T 1 And (5) numerical simulation results.
TABLE 3
Xi is defined as a relative error absolute value limiting condition of siphon starting time T' calculated by the relation between the actual siphon starting time and the length of the suspension pipe and a numerical calculation siphon starting time T, and Z is an average value of the relative error absolute values:
setting a limiting condition xi =6%, inputting initial values of alpha and beta, and obtaining Z when alpha =0.936 and beta =3.686 through programming calculation min =0.036, and a simplified calculation formula of the relation between the siphon start time and the length of the suspension pipe can be obtained by combining the above formula:
in the formula: t is 1 -siphon start time, s;
L 2 length of suspended pipe，L 2 ∈[5～150]m。
The comparison result of the siphon start time calculated by the formula and the numerical calculation is shown in table 4, and the relative error is small, so that the relation between the siphon start time of the siphon drainage system and the length of the suspension pipe can be well explained by the formula.
TABLE 4
And finally checking the length of the hanging pipe.
Assuming that the siphon drainage system of the single bucket type is installed in an important public building in Shizhuang City, each bucket has a length of a 1 Width of a 2 The slope is tan alpha, and the width of the rectangular gutter is b 1 Effective water storage height of b 2 The parameters of a rainwater hopper and a pipeline of the siphon rainwater system are the same as those of the experiment table in the third chapter,
firstly, calculating the system design displacement according to meteorological parameters and roof structures of the Hebei stone house village market:
supposing that the building is a large important public building, the rainstorm reappearance period P is selected according to 50 years, the maximum rainstorm intensity calculation formula under different reappearance period values is listed in table 5, the maximum rainstorm intensity when P =50a is calculated according to the following formula, supposing that the building adopts gutter water collection and gutter eave overflow has danger of flowing into the room, and the actual rainstorm intensity is 1.5q d And calculating the designed rainfall.
TABLE 5
In the formula: intensity of rainfall (L/s/hm) 2 ) (ii) a t is rainfall duration (min); p is the recurrence period (year).
In the formula: q. q of d Intensity of rainfall, L/s/hm 2 ；
P-rainstorm recurrence period, in which 50a is taken;
t, taking a roof rainwater drainage system for 5min when rainfall occurs;
Q d -design rain displacement, L/s;
a-catchment area, m 2 Shall be A = a 1 a 2 cosα。
Calculating to obtain the designed rainfall Q d =0.1083A, assuming a 1 ＝16m，a 2 cos α =5.5m, then Q d =9.53L/s, and the first limiting condition for calculating the length of the suspension pipe is obtained according to the relation between the actual flow and the length of the suspension pipe: should not exceed 90.03m.
Second, assume gutter width b 1 =500mm, the maximum siphon start time T is calculated according to the requirement of the specification on the siphon start time and the structural size of the gutter d ：
According to CECS183-2015 regulation:
1. the siphon starting time is not longer than 60s, and the effective water storage volume of the gutter is not smaller than the rainfall of the starting time;
expressed as: t is d A is less than or equal to 60 and a 1 b 1 b 2 ≥T d Q d
2. If the time is more than 60s or the slope of the roof is more than 2.5 percent and the gutter is full of water and overflows into the room, the effective water storage volume of the gutter is not less than the designed rainwater flow of the catchment area for 2min and is not less than the rainfall of the siphon starting time;
expressed as: if T is d A is more than or equal to 60, then a 1 b 1 b 2 ≥120Q d And a is a 1 b 1 b 2 ≥T d Q d
The relation between the actual siphon start time and the length of the suspension pipe is calculated according to the above. Calculating to obtain the length L of the suspension pipe 2 Preferably not more than 70.8m, if L is caused by too large span of the building 2 The length L of the hanging pipe can not meet the requirement, or the roof slope is more than 2.5 percent and the gutter is full of water and overflows into the room 2 Height b of effective water storage with gutter 2 The relationship of (c) is shown in fig. 3.
Suppose the effective water storage height of the gutter is b 2 =150mm, then L 2 Less than or equal to 126.11m. In summary, the second limitation on the length of the siphon drainage system suspension pipe is: it should not exceed 70.8m, and the longest should not exceed 126.11m.
By combining two limiting conditions on the length of the suspension pipe of the siphon drainage system, the final conclusion is obtained: the length of the hanging pipe of the siphon drainage system is not more than 70.8m, and the longest length is not more than 90.03m.
Claims (10)
1. The method for checking the length of the suspension pipe of the siphon drainage system is characterized by comprising the following steps
(1) Obtaining a relational expression between actual water discharge and the length of the suspension pipe by a maximum water discharge calculation method according to the length and the diameter of a pipeline of the designed siphon water discharge system and obtaining a relational expression between actual siphon starting time and the length of the suspension pipe by a siphon starting time calculation method;
(2) Calculating the designed water discharge based on the local meteorological parameter conditions and the house structure parameters;
(3) Calculating the maximum siphon starting time based on the requirements of CECS183-2015 specifications on siphon starting time and the structural size of the gutter;
(4) Obtaining a first limiting condition of the length of the suspended water pipe through the actual water displacement not less than the designed water displacement;
(5) Obtaining a second limiting condition of the length of the suspension water pipe according to the fact that the actual siphon starting time is not more than the maximum siphon starting time;
(6) And obtaining the proper length of the suspension pipe according to the first limiting condition and the second limiting condition, and checking the length of the suspension pipe for the designed siphon drainage system.
2. A method of checking the length of a syphon drain hanger pipe as claimed in claim 1, wherein said maximum displacement calculation method comprises the steps of
Obtaining a nonlinear equation of actual flow and the length of the hanging pipe through a Bernoulli equation according to known parameters of the length of a tail pipe, the length of a vertical pipe, the diameter of the tail pipe, the diameter of the hanging pipe and the diameter of the vertical pipe of a siphon drainage system pipeline;
and selecting different lengths of the suspension pipe to obtain different actual flows, and then linearizing the nonlinear equation by using a Newton iteration method to obtain a linear equation of the actual flows and the lengths of the suspension pipes.
3. A method for checking the length of a suspension pipe in a siphon drainage system according to claim 2, wherein when the diameter of the system pipe is always consistent, the nonlinear equation of the actual flow rate and the length of the suspension pipe is
Where Q is the actual flow, d j Is the diameter of the system pipeline, xi is the local resistance coefficient, k is the absolute equivalent roughness, Z 1 Is the height from the top surface of the siphon drainage system to the end surface of the water outlet.
4. A method of calibrating a length of a suspension pipe in a syphon drainage system as claimed in claim 3, wherein the step of obtaining a non-linear equation of the actual flow rate versus the length of the suspension pipe is as follows:
the flow rate of the system is determined according to the difference between the power and the resistance of the Bernoulli equation
Wherein Z is 1 From the top of the tail pipe to the bottom of the riserDistance, h 1-2 Is the loss of resistance to flow of the fluid in the pipe through the top surface of the liner to the bottom surface of the riser:
h 1-2 ＝h f +h m
the on-way resistance calculation formula adopts the following formula:
h f ＝∑RL
1
in the formula:
h f -loss of on-way resistance (mH 2O);
R-Hydraulic slope (mH 2O);
l-pipe length (m);
λ -coefficient of on-way drag;
d j -the calculated diameter (m) of the pipe;
Re-Reynolds number;
k-absolute equivalent roughness (mm);
l-pipe length (m);
γ -viscosity of water (m 2/s);
the local resistance calculation formula is as follows:
in the formula:
h m -local resistance loss (mH 2O);
xi-local resistance coefficient;
v is the flow velocity (m/s) at a certain section of the pipeline.
5. A method for checking the length of the suspended pipe of siphon drainage system as claimed in claim 2, wherein when the pipe of system has variable diameter, the relation of flow speed in each section is found out by the continuity equation, and the local resistance and the on-way resistance are calculated in sections to obtain the non-linear equation of the maximum flow rate and the length of suspended pipe.
6. A method of checking the length of a syphon drain hanger pipe as claimed in claim 2, wherein the newton's iteration is as follows: let f (Q) =0, newton's method iterative formula is:
using software programming for mathematical calculations, performing iterative calculations, specifying conditions for stopping iteration, e.g. Q k-1 -Q k Theta is allowable error, when the condition is satisfied, the calculation is stopped, and Q is considered k-1 Is the maximum displacement Q of the siphon drainage system.
7. A method of checking the length of a syphon drain hanger pipe as claimed in claim 1, wherein said syphon start-up time calculation method comprises the steps of
Defining a boundary of an upstream pipeline and a downstream pipeline in a siphon drainage system;
obtaining the volume of an upstream pipeline of the siphon drainage system according to known parameters, namely the length of a tail pipe, the upstream length of a vertical pipe, the diameter of the tail pipe, the diameter of a hanging pipe and the diameter of the vertical pipe of the siphon drainage system;
determining a relational expression between the upstream pipeline filling time and the actual flow according to the volume of the upstream pipeline;
defining a correction relational expression of siphon starting time and upstream pipeline filling time, and substituting the relational expression of the upstream pipeline filling time and actual flow into the correction relational expression;
and selecting different lengths of the suspension pipe to obtain different actual flows, obtaining a correction coefficient in a correction relation, and finally obtaining a linear equation of the siphon starting time and the suspension pipe.
8. A method of checking the length of a syphon drain hanger pipe as claimed in claim 7, wherein the upstream pipe fill time is related to the actual flow rate by
Wherein
The correction relation between the siphon start time and the upstream pipeline filling time is T C ＝αT C +β
Wherein, T C For upstream pipe fill time, V is upstream pipe volume, Q is actual flow, V 1 Volume of tail pipe, V 2 Is the volume of the suspension pipe, V 3 Is the volume of the stand pipe, d 1 Is the diameter of the tail pipe, d 2 Is the diameter of the suspended pipe, d 3 Is the diameter of the stand pipe; l is a radical of an alcohol 1 Is the length of tail pipe, L 2 To the length of the suspension tube, L 3 Both α and β are correction factors for riser length.
9. A method of calibrating a length of a siphon drain system hanger pipe according to claim 1, wherein the design discharge is calculated based on the years of the heavy rain return period, the actual intensity of the heavy rain, the duration of the rain fall, and the catchment area as known parameters.
10. A method of calibrating the length of a siphon drain suspension pipe according to claim 1, wherein in step (3) the CECS183-2015 specification specifies a rainfall for which siphon start time should not exceed 60s and effective impounded volume of gutter should not be less than start time;
if the time is more than 60s or the slope of the roof is more than 2.5 percent and the gutter is full of water and overflows into the room, the effective water storage volume of the gutter should not be less than the designed rainwater flow of the catchment area for 2min and should not be less than the rainfall of the siphon start time.
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