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渣漿泵的相似定律及比轉數    兩臺泵相似，嚴格的講必須滿足兩臺泵幾何相似，液流運動相似和液流動力相似。

(1)幾何相似:即兩臺泵過流部件相似點的各角度相等，同名尺寸比值相等。即:
式中，注腳“p”為實型泵;“m”為模型泵;
     L----任 意點的相應線性尺寸。
    (2)液體運動相似:就是兩臺泵內相應點的液體流速方向相同，大小成同一比例。 即:
    (3) 液體動力相似:就是作用在兩臺泵相應點液體上的同名力(如慣性力、黏性力、重力)的比值相等。
    實際上兩臺泵要同時滿足上述三個條件是困難的，在實際應用時，常忽略了一些次要因素。由于泵中的流速較高，處于阻力平方區，所以通常在泵中不考慮動力相似。
    離心泵的工況點是用它的性能參數表表示的，在相似工況下，兩臺相似泵有如下關系:即泵的流量Q相似定律，泵的揚程H相似定律，泵的功率相似定律。
1.流量相似定律

泵的流量:根據式(2-13) 可用下式表示:

兩臺相似泵的流量關系可用下式表示:

由于兩臺泵相似，則有

由于在相似工況運行，必然運動相似。所以
故式(2-30)可寫為

這就是泵流量相似定律。

2.揚程相似定律

由式(2-14)及式(2-25)，兩臺相似泵的揚程關系可用下式表示:

由于兩臺泵運動相似，必然滿足
代入上式(2-32)可得

這就是泵揚程相似定律。

3.功率相似定律

由式(2-6)可得兩臺相似泵的功率關系式:

將式(2-31)， 式(2-33)及η=nn7.m代入式(2-34)得

這就是泵功率相似定律。

當實型泵與模型泵的尺寸比例相差不太大時，為了簡化問題起見，認為模型泵與實型泵的效率相等，即ηp = Twm，Tnp=7im，p=mm，于是可得:

式中，注腳“p”表示實型來，注腳“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進行試驗，然后將模型泵的實驗結果換算成實行泵的性能。但是當兩尺寸相差很大時，誤差會較大，需參考有關資料來進行修正。

當同一 臺泵輸送同一種液體時在
則有

這就是泵的比例定律，在泵的調節中就用改變轉速來改變泵的性能，用式(2 - 39)、式(2-40)、式(2-41) 來計算改變轉速后泵的性能。在試驗中，當試驗設備受到限制時，可用降速試驗，然后用上式進行換算泵的性能。
二、 泵的比轉數π。

1.比轉數n。的得出
相似工況下，由式(2-36) 及式(2-37)可得:

將式(2-42)兩端平方，式(2-43) 兩端立方，然后相除消去D，再開四次方可得到:

即兩臺相似的泵，將相應的工況下的性能參數代入式(2 -44)，計算出來的數值是相同的，把這個數值稱為泵的比轉數nq:
    ng就有這樣的性質，對一系列幾何相似的泵，在相似的工況下ng值都相等，也即na相等，兩臺泵就幾何相似，ng 就是相似泵的相似準則。
    在我國為了使與水輪機的比轉數一致， 將上面公式乘以一個數3.65 ，則泵的比轉數n。為:

ns與ng本質上沒有任何區別，只是數值上不同，我國長久以來已經習慣使用n,，歐美國家常用ne,由于各國使用的單位不一致，所以同一臺泵算出來的比轉數值是不一樣的。
2.比轉數n、計算注意事項
    (1)同一臺泵在不同工況下具有不同的n。值，作為相似準則的n.是指對應最高效率點工況(即設計工況)的n。值。
    (2)雙吸泵比轉數的計算:因為比轉數是對葉輪而言的，雙吸泵實際是將兩個單吸葉輪背靠背的裝在一起并聯工作，所以雙吸泵的比轉數n。
    (3)多級泵比轉數的計算:因為多級泵相當于將幾個單級泵的葉輪裝在一根軸上，串聯工作，所以多級泵的比轉數n,應用單級揚程來計算。
3. 比轉數n。的用處
    (1)利用比轉數n.對葉輪進行分類和分析性能變化狀況

比轉數ns的大小與時輪形狀和泵性能曲線形狀有密切關系，如表2-3所示。比轉數ns越小，D2/D0值越大，葉輪流道相對地越細長，葉片為圓柱規葉片不扭曲；Q-H曲線比較平坦: Q-P曲線隨流量Q增大功率P上升得比較快: Q-η曲線高效區比較寬，但最高效率m比較低。
    隨比轉數n。逐漸增大，D2/D。 值變小，葉輪流道越來越寬，葉片進口處開始變扭曲;Q- H曲線也越來越陡;當n。 大到一定值時葉輪出口邊就傾斜了，成了混流泵，葉片從進口到出口都變成扭曲;Q -H曲線開始出現s形曲線; Q-P曲線隨流量Q增大功率P上升得比較慢，當n。大到一定值時功率P隨流量Q的增大不再增大或稍有下降。Q一η曲線高效區變窄，但最高效率增高，在n。 = 120 時能得到最好的效率值，當n。> 180后，隨n。增加，最高效率7m反而有所降低。 渣漿泵

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