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渣漿泵串聯的解析法

設兩臺離心泵串聯工作，分別由兩臺泵實測或泵特性曲線上取點得到幾組揚程.流量數據.用最小二乘祛回歸得到泵的特性方程分別為:
式中的系數a1、b1、a2、b2可由式(1 - 69)計算得到。
    按照兩泵串聯后的總揚程等于兩泵在同一流量時的揚程之和，即Q=Ql=Qll時Hl+ll= Hl+ Hll的原則，有:則兩臺相同泵串聯后的特性方程為:

H=A-BQ2
將其與管路特性方程聯立，即可解得系統工作點。多臺離心泵串聯工作也可按此原則進行計算。

3.復雜管路系統工作點的確定

對于復雜管路系統來說，根據水力特點，并聯時管路交叉點的壓力相等，總流量等于各支管流量之和；串聯時各管段流量相等，總摩阻等于各管段摩阻之和進行疊加。對于交匯及分支管路系統，求解過程如下。

1) 泵在分支管路上工作的裝置特性

經過一臺泵(或幾臺泵申聯、并聯)將油品同時輸往一處或幾處時，要采取分支管路來工作，如圖1- 48(a)所示。油品由管1經過泵后再沿管2和管3分別輸送到兩油罐內。三個油罐中液面對于泵軸線的標高差為z1、z2和z3。

(1) 圖解法。

畫出吸入管路特性(h-Q)1以及排出管路的特性(h-Q)2和(h-Q)3。因管2和管3是并聯工作,需按并聯相加得管路特性(h-Q)2+3。然后再和(h-Q)1串聯相加，得到整個管路系統的總管路特性(h-Q)at ,它和泵的性能曲線H-Q相交于M點，即為分支管路的工作點。

M點相應的流量Qw就是管1中的流量Q。為確定管2和管3中的流量，過M點作垂線與管路特性(h-Q)2+3相交于A點,從A點引水平線與(h Q)2相交于點2，與(h-Q)3相交于點3，則點2和點3相應的流量Q2和Q3即為管2和管3中的流量,并且Qm=Qa=Q2+Q3=Q1。

(2) 解析法。

由泵實測或泵特性曲線上取點得到幾組揚程、流量數據,用最小二乘法回歸得到泵的特性方程為H=a-bQ2，系數a、b可由式(1- 69)計算得到。
管路1的特性方程為:

管路2的特性方程為:
                        h2=z2+k2Q2

管路3的特性方程為:

h3=z3+k3Q3
管路2和管路3先并聯然后與管路1串聯，根據管道并聯原則有:
h2=h3, Q=Q1=Q2 + Q3
管路總特性為:
h=h1 +h2或h=h1 + h3

對于系統來說:

h= H,Q1 =Q渣漿泵廠家

解方程組即可求得Q1、Q2、Q3。

Analytical method of slurry pump in series
Two centrifugal pumps are designed to work in series, and several groups of head and flow data are obtained from the measured data of two pumps or the points on the pump characteristic curve. The characteristic equations of pumps are obtained by least square regression
The coefficients A1, B1, A2 and B2 in the formula can be calculated by formula (1-69).
According to the principle that the total head of two pumps in series is equal to the sum of the heads of two pumps at the same flow, that is, when q = QL = QLL, HL + ll = HL + HL, the characteristic equation of two pumps in series is as follows:
H=A-BQ2
The working point of the system can be obtained by combining it with the characteristic equation of pipeline. Several centrifugal pumps in series can also be calculated according to this principle.
3. Determination of working point of complex pipeline system
For the complex pipeline system, according to the hydraulic characteristics, the pressure at the crossing point of the pipeline is equal in parallel, and the total flow is equal to the sum of the flow of each branch pipe; the flow of each pipe section is equal in series, and the total friction is equal to the sum of the friction of each pipe section for superposition. For the intersection and branch pipeline system, the solution process is as follows.
1) Device characteristics of pump working on branch pipeline
When oil products are transported to one or several places at the same time through one pump (or several pumps applying for connection or parallel connection), branch pipeline shall be adopted for operation, as shown in Fig. 1-48 (a). The oil is pumped by tube 1 and then transported to two oil tanks along tube 2 and tube 3 respectively. The elevation difference of the three oil tanks to the pump axis is Z1, Z2 and Z3.
(1) Graphic method.
Draw the characteristics of suction line (H-Q) 1 and discharge line (H-Q) 2 and (H-Q) 3. Because tube 2 and tube 3 work in parallel, it is necessary to add the characteristics (H-Q) 2 + 3 in parallel. Then add (H-Q) 1 in series to get the total pipeline characteristic (H-Q) at of the whole pipeline system. It intersects the performance curve H-Q of the pump at point m, which is the working point of the branch pipeline.
The corresponding flow QW at point m is the flow Q in tube 1. In order to determine the flow in pipe 2 and pipe 3, make a vertical line through point m to intersect with the pipeline characteristic (H-Q) 2 + 3 at point a, lead the horizontal line from point a to intersect with (H q) 2 at point 2, and intersect with (H-Q) 3 at point 3, then the corresponding flow Q2 and Q3 at point 2 and point 3 are the flow in pipe 2 and pipe 3, and QM = QA = Q2 + Q3 = Q1.
(2) Analytical method.
Several groups of head and flow data are obtained from the measured pump or the points on the pump characteristic curve. The characteristic equation of the pump is h = a-bq2 by least square regression. The coefficients a and B can be calculated by formula (1-69).
The characteristic equation of pipeline 1 is as follows:
The characteristic equation of pipeline 2 is:
H2=z2+k2Q2
The characteristic equation of pipeline 3 is as follows:
H3=z3+k3Q3
Pipeline 2 and pipeline 3 are connected in parallel and then in series with pipeline 1. According to the principle of pipeline parallel connection, they are as follows:
h2=h3, Q=Q1=Q2 + Q3
The general characteristics of the pipeline are:
H = H1 + H2 or H = H1 + H3
For the system:
H = h, Q1 = q slurry pump manufacturer
Q1, Q2 and Q3 can be obtained by solving the equations.