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渣漿泵并聯的解析法

設兩臺離心泵并聯工作，分別由兩臺泵實測或泵特性曲線上取點得到的幾組揚程、流量數據,用最小二乘法回歸得到泵的特性方程分別為:
式中的系數a1、b、a2、b2可由式(1- 69)計算得到。
    按照每臺泵提供的揚程相同，均等于總揚程，總流量為每臺泵的流量之和的原則,有:
                           H=Hl=Hll

Q=Ql + Qll
若為兩臺性能相同的泵，即a=a1=a2,b=b1=b2,Q1 =Qll=Q2，則有:

則兩臺相同泵并聯后的特性方程為:

H= A- BQ2

將其與管路特性方程聯立，即可解得系統工作點。不同性能的泵并聯工作及多臺離心泵并聯工作也可按此原則進行計算。
2.離心泵串聯工作
    串聯是指前面一臺泵的出口向后面一臺泵的入口輸送液體的工作方式，常用于提高泵的揚程,增加輸送距離,減少泵站數量，或提高揚程以增加流量的工況中。

串聯也分為相同性能泵的串聯工作與不同性能泵的串聯工作，分別討論如下。

1) 相同性能的泵串聯

如圖1- 45所示,(H - Q)、(H- Q)n為兩臺相同性能泵的性能曲線。根據流體力學原理,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:=Q時H= H + h兩泵串聯后的總性能曲線等于兩泵性能曲線在同一流量下揚程逐點疊加起來 .即圖1- 45中的(H- Q)-r曲線。可見，泵串聯后揚程性能曲線向上移動，使同一流量下的揚程提高了。
    假設管路特性h-Q不變(忽略兩泵串聯后管路特性的變化)時,兩泵串聯后總性能曲線(H-Q)1→日與管路特性曲線的交點為M,M點即串聯后的工作點。該點的揚程為Hl+ll=Hl+ Hll，流量Q1+1  = Q1=Q1。為確定每臺泵的工作點，自M點作垂線，交單泵性能曲線(H-Q).n于A點，由圖可知，泵I的流量Q等于泵I中流量Qll，也等于串聯后流量。在此流量下，兩泵提供相同揚程HI=HII，液體具有的總揚程HI+II=HI+HII=2HI。若每臺泵單獨在管路中工作時，泵的工作點為M，.則串聯后的總揚程低于泵單獨工作時揚程的2倍,而流量卻大于單泵工作的流量。其原因是由于串聯后的揚程提高了，但管路裝置未變，多余的能量使流速加快，流量增加。
    渣漿泵串聯工作時，因后面一臺泵承受的壓力較高，故應注意其殼體的強度和密封等問題。啟動和停泵時也要按順序操作，啟動前，將各串聯泵出口網都關閉，啟動第一臺泵后再開第一臺泵出口調節閥，然后啟動第二臺泵，再打開第二臺泵的出口閥向管道輸送液體。此外，與串聯泵一起工作的管路特性陡峭度越陡越能增大串聯后的揚程。實際上，幾臺泵串聯工作相當于一臺多級泵，而一臺多級泵在結構上比多臺性能相同的離心泵串聯要緊湊得多,安裝維修也方便得多，因而應選用多級泵代替串聯泵使用。

Analytical method for parallel connection of slurry pump
Two centrifugal pumps are designed to work in parallel, and several groups of head and flow data are obtained from the actual measurement of two pumps or points on the pump characteristic curve respectively. The characteristic equations of pumps are obtained by least square regression
The coefficients A1, B, A2 and B2 in the formula can be calculated by formula (1-69).
According to the principle that the head provided by each pump is the same and equal to the total head, and the total flow is the sum of the flow of each pump, there are:
H=Hl=Hll
Q=Ql + Qll
If there are two pumps with the same performance, i.e. a = A1 = A2, B = B1 = B2, Q1 = QLL = Q2, there are:
Then the characteristic equation of two pumps in parallel is:
H= A- BQ2
The working point of the system can be obtained by combining it with the characteristic equation of pipeline. The parallel operation of pumps with different performance and the parallel operation of multiple centrifugal pumps can also be calculated according to this principle.
2. Centrifugal pump works in series
Series connection refers to the working mode in which the outlet of the previous pump delivers liquid to the inlet of the latter pump. It is often used to increase the pump head, increase the delivery distance, reduce the number of pump stations, or increase the head to increase the flow.
The series work can also be divided into the series work of the same performance pump and the series work of different performance pumps, which are discussed as follows.
1) Pumps of the same performance in series
As shown in Figure 1-45, (H-Q) and (H-Q) n are the performance curves of two pumps with the same performance. According to the principle of hydrodynamics, 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, the total performance curve of two pumps in series when h = H + h at Q: = q is equal to the superposition of the heads of two pumps at the same flow point by point, that is, (H-Q) - R curve in Figure 1-45. It can be seen that the performance curve of pump head moves upward after series connection, which improves the head under the same flow.
Assuming that the pipeline characteristic H-Q remains unchanged (ignoring the change of the pipeline characteristic after the two pumps are connected in series), the intersection point of the total performance curve (H-Q) 1 → day and the pipeline characteristic curve after the two pumps are m, and m point is the working point after the series. The head of this point is HL + ll = HL + HL, and the flow Q1 + 1 = Q1 = Q1. In order to determine the working point of each pump, make a vertical line from point m, and submit the single pump performance curve (H-Q). N to point A. It can be seen from the figure that the flow Q of pump I is equal to the flow QLL in pump I and the flow after series connection. Under this flow, the two pumps provide the same lift hi = HII, and the total lift hi + II = hi + HII = 2hi for the liquid. If the working point of each pump is m when it works in the pipeline alone, the total head after series connection is less than 2 times of the head when it works alone, while the flow is greater than the flow of single pump. The reason is that the lift after series connection is increased, but the pipeline device remains unchanged, and the excess energy makes the flow speed faster and the flow rate increased.
When the slurry pump works in series, the strength and sealing of its shell should be paid attention to because the pressure of the latter pump is higher. Start and stop the pump in sequence. Before starting, close the outlet network of each series pump. After starting the first pump, open the outlet regulating valve of the first pump, then start the second pump, and then open the outlet valve of the second pump to deliver liquid to the pipeline. In addition, the steeper the characteristic of the pipeline working with the series pump is, the higher the lift of the series pump is. In fact, several pumps in series work as one multistage pump, and one multistage pump is much more compact in structure than many centrifugal pumps with the same performance in series, so it is much more convenient to install and maintain, so multistage pump should be used instead of series pump.