渣浆泵的相似定律及比转数    两台泵相似，严格的讲必须满足两台泵几何相似，液流运动相似和液流动力相似。

(1)几何相似:即两台泵过流部件相似点的各角度相等，同名尺寸比值相等。即:
式中，注脚“p”为实型泵;“m”为模型泵;
     L----任 意点的相应线性尺寸。
    (2)液体运动相似:就是两台泵内相应点的液体流速方向相同，大小成同一比例。 即:
    (3) 液体动力相似:就是作用在两台泵相应点液体上的同名力(如惯性力、黏性力、重力)的比值相等。
    实际上两台泵要同时满足上述三个条件是困难的，在实际应用时，常忽略了一些次要因素。由于泵中的流速较高，处于阻力平方区，所以通常在泵中不考虑动力相似。
    离心泵的工况点是用它的性能参数表表示的，在相似工况下，两台相似泵有如下关系:即泵的流量Q相似定律，泵的扬程H相似定律，泵的功率相似定律。
1.流量相似定律

泵的流量:根据式(2-13) 可用下式表示:

两台相似泵的流量关系可用下式表示:

由于两台泵相似，则有

由于在相似工况运行，必然运动相似。所以
故式(2-30)可写为

这就是泵流量相似定律。

2.扬程相似定律

由式(2-14)及式(2-25)，两台相似泵的扬程关系可用下式表示:

由于两台泵运动相似，必然满足
代入上式(2-32)可得

这就是泵扬程相似定律。

3.功率相似定律

由式(2-6)可得两台相似泵的功率关系式:

将式(2-31)， 式(2-33)及η=nn7.m代入式(2-34)得

这就是泵功率相似定律。

当实型泵与模型泵的尺寸比例相差不太大时，为了简化问题起见，认为模型泵与实型泵的效率相等，即ηp = Twm，Tnp=7im，p=mm，于是可得:

式中，注脚“p”表示实型来，注脚“m表示模型泵。

利用以上相似定律，大型泵可以做成小的模型泵进行试验，然后将模型泵的实验结果换算成实行泵的性能。但是当两尺寸相差很大时，误差会较大，需参考有关资料来进行修正。

当同一 台泵输送同一种液体时在
则有

这就是泵的比例定律，在泵的调节中就用改变转速来改变泵的性能，用式(2 - 39)、式(2-40)、式(2-41) 来计算改变转速后泵的性能。在试验中，当试验设备受到限制时，可用降速试验，然后用上式进行换算泵的性能。
二、 泵的比转数π。

1.比转数n。的得出
相似工况下，由式(2-36) 及式(2-37)可得:

将式(2-42)两端平方，式(2-43) 两端立方，然后相除消去D，再开四次方可得到:

即两台相似的泵，将相应的工况下的性能参数代入式(2 -44)，计算出来的数值是相同的，把这个数值称为泵的比转数nq:
    ng就有这样的性质，对一系列几何相似的泵，在相似的工况下ng值都相等，也即na相等，两台泵就几何相似，ng 就是相似泵的相似准则。
    在我国为了使与水轮机的比转数一致， 将上面公式乘以一个数3.65 ，则泵的比转数n。为:

ns与ng本质上没有任何区别，只是数值上不同，我国长久以来已经习惯使用n,，欧美国家常用ne,由于各国使用的单位不一致，所以同一台泵算出来的比转数值是不一样的。
2.比转数n、计算注意事项
    (1)同一台泵在不同工况下具有不同的n。值，作为相似准则的n.是指对应最高效率点工况(即设计工况)的n。值。
    (2)双吸泵比转数的计算:因为比转数是对叶轮而言的，双吸泵实际是将两个单吸叶轮背靠背的装在一起并联工作，所以双吸泵的比转数n。
    (3)多级泵比转数的计算:因为多级泵相当于将几个单级泵的叶轮装在一根轴上，串联工作，所以多级泵的比转数n,应用单级扬程来计算。
3. 比转数n。的用处
    (1)利用比转数n.对叶轮进行分类和分析性能变化状况

比转数ns的大小与时轮形状和泵性能曲线形状有密切关系，如表2-3所示。比转数ns越小，D2/D0值越大，叶轮流道相对地越细长，叶片为圆柱规叶片不扭曲；Q-H曲线比较平坦: Q-P曲线随流量Q增大功率P上升得比较快: Q-η曲线高效区比较宽，但最高效率m比较低。
    随比转数n。逐渐增大，D2/D。 值变小，叶轮流道越来越宽，叶片进口处开始变扭曲;Q- H曲线也越来越陡;当n。 大到一定值时叶轮出口边就倾斜了，成了混流泵，叶片从进口到出口都变成扭曲;Q -H曲线开始出现s形曲线; Q-P曲线随流量Q增大功率P上升得比较慢，当n。大到一定值时功率P随流量Q的增大不再增大或稍有下降。Q一η曲线高效区变窄，但最高效率增高，在n。 = 120 时能得到最好的效率值，当n。> 180后，随n。增加，最高效率7m反而有所降低。 渣浆泵

Similarity law of pump

The two pumps are similar. Strictly speaking, the geometry of the two pumps must be similar, the movement of the liquid flow is similar and the power of the liquid flow is similar.

(1) geometric similarity: that is to say, the angles of the similar parts of the two pumps are equal, and the size ratio of the same name is equal. Namely:

In the formula, "P" is the solid pump; "m" is the model pump;

L - corresponding linear dimension of any point.

(2) similar liquid movement: that is, the flow velocity direction of the corresponding points in the two pumps is the same, and the size is in the same proportion. Namely:

(3) liquid dynamic similarity: it means that the ratio of the same name force (such as inertia force, viscosity force and gravity) acting on the corresponding point liquid of two pumps is equal.

In fact, it is difficult for two pumps to meet the above three conditions at the same time. In practical application, some secondary factors are often ignored. Due to the high flow rate in the pump, which is in the resistance square area, the dynamic similarity is usually not considered in the pump.

The working point of centrifugal pump is expressed by its performance parameter table. Under similar working conditions, two similar pumps have the following relations: the flow Q similar law of pump, the head h similar law of pump, and the power similar law of pump.

1. Flow similarity law

Pump flow: according to formula (2-13), it can be expressed as follows:

The flow relationship of two similar pumps can be expressed as follows:

Since the two pumps are similar, there are

Because it operates under similar working conditions, it will inevitably move in the same way. therefore

Therefore, formula (2-30) can be written as

This is the law of pump flow similarity.

2. Law of head similarity

From equations (2-14) and (2-25), the head relationship of two similar pumps can be expressed as follows:

Because the two pumps have similar movement, it is necessary to meet

Substitute the above formula (2-32) to get

This is the law of pump head similarity.

3. Power similarity law

The power relationship of two similar pumps can be obtained from equation (2-6):

By substituting equation (2-31), equation (2-33) and η = nn7. M into equation (2-34), we can get

This is the law of pump power similarity.

When the size ratio of the real pump and the model pump is not too large, in order to simplify the problem, it is considered that the efficiency of the model pump and the real pump is equal, that is, η P = TWM, TNP = 7im, P = mm, so we can get:

In the formula, "P" means real type, and "m" means model pump.

Using the above similarity law, large pump can be made into small model pump for test, and then the experimental results of model pump can be converted into the performance of pump. However, when there is a large difference between the two dimensions, the error will be large, so it is necessary to refer to the relevant information for correction.

When the same pump delivers the same liquid

Then there are

This is the proportional law of the pump. In the regulation of the pump, change the speed to change the performance of the pump. Use formula (2-39), formula (2-40) and formula (2-41) to calculate the performance of the pump after changing the speed. In the test, when the test equipment is limited, the speed reduction test can be used, and then the above formula can be used to convert the performance of the pump.

2. Specific speed π of pump.

1. Specific speed n. Draw

Under similar working conditions, formula (2-36) and formula (2-37) can be used to obtain:

Square the two ends of formula (2-42) and cube the two ends of formula (2-43), then divide and eliminate D, and then open the fourth power to get:

That is to say, for two similar pumps, the performance parameters under corresponding working conditions are substituted into equation (2-44), and the calculated value is the same, which is called the specific speed of pump NQ:

Ng has such a property. For a series of pumps with similar geometry, under similar working conditions, ng values are equal, that is, Na is equal. Two pumps are geometrically similar, and ng is the similarity criterion of similar pumps.

In our country, in order to make the specific speed consistent with the turbine, multiply the above formula by a number of 3.65, then the specific speed of the pump n. For:

In essence, there is no difference between ns and ng, but the numerical value is different. China has been used to use n for a long time. European and American countries often use ne. Because the units used in different countries are different, the specific rotation calculated by the same pump is different.

2. Specific speed n. precautions for calculation

(1) the same pump has different N under different working conditions. Value, as the similarity criterion, N. refers to n corresponding to the highest efficiency point condition (i.e. design condition). Value.

(2) calculation of the specific speed of double suction pump: because the specific speed is for the impeller, the double suction pump actually installs two single suction impellers back-to-back and works in parallel, so the specific speed of the double suction pump is n.

(3) calculation of specific speed of multistage pump: because multistage pump is equivalent to installing several impellers of single-stage pump on a shaft and working in series, the specific speed of multistage pump n shall be calculated by single-stage head.

3. Specific speed n. Usefulness

(1) use specific speed n. classify impeller and analyze performance change

The specific speed ns is closely related to the shape of the time wheel and the shape of the pump performance curve, as shown in table 2-3. The smaller the specific speed ns is, the larger the D2 / d0 value is, the more slender the impeller passage is, and the blade is cylindrical gauge blade without distortion; the Q-H curve is relatively flat; the Q-P curve rises faster with the increase of flow Q; the efficient area of q-η curve is wider, but the highest efficiency m is lower.

With specific revolution n. Gradually increased, D2 / d The smaller the value, the wider the impeller channel, the more twisted the blade inlet; the steeper the Q-H curve; when n When it reaches a certain value, the outlet edge of the impeller inclines and becomes a mixed flow pump, and the blades become twisted from the inlet to the outlet; the Q-H curve begins to show a S-shaped curve; the Q-P curve increases slowly with the flow Q, and the power P increases slowly when n. At a certain value, the power P will not increase or decrease slightly with the increase of flow Q. The efficient region of q-η curve narrowed, but the highest efficiency increased at n =The best efficiency value can be obtained at 120, when n. >After 180, with n. However, the highest efficiency of 7 m decreased Slurry pump