a 2. Kinematic similitude defination The corresponding parameters of motion of prototype such as velocity, acceleration are consistent in direction and in proportion to magnitude to those of model called kinematic similitude Time scale 6 (4-4) Velocity scale (45) Acceleration scale OD amt (46)
11 2. Kinematic similitude Time scale m n t t t = （4—4） Velocity scale t l m m n n m n t l t l = = = （4—5） Acceleration scale 2 2 2 t l m m n n m n t l t l a a = = = （4—6） The corresponding parameters of motion of prototype such as velocity, acceleration are consistent in direction and in proportion to magnitude to those of model called kinematic similitude . defination：
相似量筑分 二、运动相似 定义: 原型与模型中对应的运动参数如速度、加速度方向一致, 大小成比例,称为运动相似。 时间比尺为 (4-4) 速度比尺为== (45) 加速度比尺为9= (46) m 12
12 二 、 运动相似 时间比尺为 m n t t t = （4—4） 速度比尺为 t l m m n n m n t l t l = = = （4—5） 加速度比尺为 2 2 2 t l m m n n m n t l t l a a = = = （4—6） 原型与模型中对应的运动参数如速度、加速度方向一致， 大小成比例，称为运动相似。 定义：
Similarity Principle and Dimension Analyse 3. Dynamic similarity a defination The forces of corresponding points of prototype and model are consistent in direction and in proportion to magnitude that is called dynamic similarit Density scale 8 =pn (47) Mass scale 5= p, V (48) pm/m Force scale OFF E="n=6n2=022(49) 13
13 3. Dynamic similarity Density scale m n = （4—7） Mass scale 3 l m m n n m n m V V m m = = = （4—8） Force scale 2 2 m a l m m n n m n F m a m a F F = = = = （4—9） The forces of corresponding points of prototype and model are consistent in direction and in proportion to magnitude that is called dynamic similarity . defination：
、动力相似 定义: 原型与模型中对应点处受力方向相同、大小成比例,称为 动力相似。 密度比尺为8=Pn (4—7) p, V 质量比尺为δmmmO (48) 力的比尺为6===0n6=8282(49) 14
14 三 、 动力相似 密度比尺为 m n = （4—7） 质量比尺为 3 l m m n n m n m V V m m = = = （4—8） 力的比尺为 2 2 m a l m m n n m n F m a m a F F = = = = （4—9） 原型与模型中对应点处受力方向相同、大小成比例，称为 动力相似。 定义：
a Unit mass scale g (410) g according to (49) A=2h2 mm m F That is 22 12b (411) m n m In formula is a dimensionless number called Newton number, denoted by Ne So formula (411) change to Ne en= Ne (412) That is, two geometry similitude flows, if dynamic similarity then their Newton number must be equal; Whereas two geometry similitude flows whose Newton number are equal, their dynamic similarity must be equal. So geometry similitude is only necessary condition of similitude, and that kinematic similitude and dynamic similarity are necessary and sufficient condition of similitude 15
15 Unit mass scale m n g g g = （4—10） according to（4—9） 2 2 2 2 m m m n n n m n l l F F = That is 2 2 2 2 m m m m n n n n l F l F = （4—11） In formula， is a dimensionless number ,called Newton number ，denoted by 2 2 l F Ne Nen = Nem （4—12） That is, two geometry similitude flows, if dynamic similarity, then their Newton number must be equal; Whereas, two geometry similitude flows whose Newton number are equal, their dynamic similarity must be equal. So geometry similitude is only necessary condition of similitude ，and that kinematic similitude and dynamic similarity are necessary and sufficient condition of similitude. So formula（4—11）change to