渣浆泵并联的解析法

设两台离心泵并联工作，分别由两台泵实测或泵特性曲线上取点得到的几组扬程、流量数据,用最小二乘法回归得到泵的特性方程分别为:
式中的系数a1、b、a2、b2可由式(1- 69)计算得到。
    按照每台泵提供的扬程相同，均等于总扬程，总流量为每台泵的流量之和的原则,有:
                           H=Hl=Hll

Q=Ql + Qll
若为两台性能相同的泵，即a=a1=a2,b=b1=b2,Q1 =Qll=Q2，则有:

则两台相同泵并联后的特性方程为:

H= A- BQ2

将其与管路特性方程联立，即可解得系统工作点。不同性能的泵并联工作及多台离心泵并联工作也可按此原则进行计算。
2.离心泵串联工作
    串联是指前面一台泵的出口向后面一台泵的入口输送液体的工作方式，常用于提高泵的扬程,增加输送距离,减少泵站数量，或提高扬程以增加流量的工况中。

串联也分为相同性能泵的串联工作与不同性能泵的串联工作，分别讨论如下。

1) 相同性能的泵串联

如图1- 45所示,(H - Q)、(H- Q)n为两台相同性能泵的性能曲线。根据流体力学原理,两泵串联后的总扬程等 于两泵在同一流量时的扬程之和，即Q:=Q时H= H + h两泵串联后的总性能曲线等于两泵性能曲线在同一流量下扬程逐点叠加起来 .即图1- 45中的(H- Q)-r曲线。可见，泵串联后扬程性能曲线向上移动，使同一流量下的扬程提高了。
    假设管路特性h-Q不变(忽略两泵串联后管路特性的变化)时,两泵串联后总性能曲线(H-Q)1→日与管路特性曲线的交点为M,M点即串联后的工作点。该点的扬程为Hl+ll=Hl+ Hll，流量Q1+1  = Q1=Q1。为确定每台泵的工作点，自M点作垂线，交单泵性能曲线(H-Q).n于A点，由图可知，泵I的流量Q等于泵I中流量Qll，也等于串联后流量。在此流量下，两泵提供相同扬程HI=HII，液体具有的总扬程HI+II=HI+HII=2HI。若每台泵单独在管路中工作时，泵的工作点为M，.则串联后的总扬程低于泵单独工作时扬程的2倍,而流量却大于单泵工作的流量。其原因是由于串联后的扬程提高了，但管路装置未变，多余的能量使流速加快，流量增加。
    渣浆泵串联工作时，因后面一台泵承受的压力较高，故应注意其壳体的强度和密封等问题。启动和停泵时也要按顺序操作，启动前，将各串联泵出口网都关闭，启动第一台泵后再开第一台泵出口调节阀，然后启动第二台泵，再打开第二台泵的出口阀向管道输送液体。此外，与串联泵一起工作的管路特性陡峭度越陡越能增大串联后的扬程。实际上，几台泵串联工作相当于一台多级泵，而一台多级泵在结构上比多台性能相同的离心泵串联要紧凑得多,安装维修也方便得多，因而应选用多级泵代替串联泵使用。

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.