1' The straight line parallel to one side of the triangle intersects with the other two sides (or extension lines of both sides), and the triangle formed is similar to the original triangle;

2' If two angles of a triangle are equal to two angles of another triangle, then the two triangles are similar.

3' Two triangles are similar. If the ratio of the corresponding sides of the two groups is equal, the corresponding included angles are also equal.

If the proportions of three groups of corresponding edges are equal, two triangles are similar.

Two triangles with equal angles and proportional sides are called similar triangles.

Similar conditions of centrifugal pump impeller

1. Flow similarity relation

Pump impellers with similar geometries have the same outlet displacement coefficient.

If the size ratio is not very large, ηv = η'v for centrifugal pumps satisfying three similar conditions.

You can get it:

2. Head similarity

3. Power similarity relation

The above formula expresses the relationship between the main performance parameters of centrifugal pumps that meet three similar conditions, which is called the three laws of similarity.

similarity theory

Similarity theory is widely used in pump design and test. Similarity design and model test based on model transformation are carried out under the guidance of similarity theory. According to the similarity theory, the experimental results of the model can be converted into the real pump, and the parameters of the real pump can also be converted into the parameters of the model for model design and experiment.

It is much more economical to do experiments with small models than with real machines. Moreover, due to the limitation of conditions, it is often difficult to experiment with the real machine when the size of the real machine is too large, the rotating speed is too high or the special liquid such as high temperature is pumped, so the model experiment can only be used instead.

① Geometric similarity

The two pumps are completely similar in structure, with the same corresponding size ratio, the same number of blades and the same corresponding angle.

② Motion similarity

The liquid flow at the corresponding points in the two pumps is similar, and the ratio of speed and direction is the same (that is, the speed triangle is similar).

Motion similarity is the inevitable result of geometric similarity and dynamic similarity.

③ Dynamic similarity

The ratio of liquid inertia force and viscous force at the corresponding points in the two pumps is the same.

Satisfy the above three items, both pumps are similar. Generally, as long as two pumps meet the geometric similarity and motion similarity, they are considered to meet the similarity conditions.

Similarity law

Two pumps meeting similar conditions can be approximately considered to be equal in volumetric efficiency, hydraulic efficiency and mechanical efficiency. At this time, the following types are established, which is called similarity law.