Similitude is defined as the similarity between the model and its prototype in every respect, which means the model and prototype have similar properties or model and prototype are completely similar. Three types of similarities must exist between the mode and prototype. They are:
1. Geometric Similarity
2. Kinetic Similarity
3. Dynamic Similarity .
1:) Geometric similarity :
The Geometric similarity is said to exist between the model and the prototype. The ratio of all corresponding linear dimensions in the model and prototype are equal.
2:) Kinematic similarity :
Kinematic Similarity means the Similarity of motion between model and prototype. Thus kinematic similarity said to exist between the model and the prototype if the ratios of the velocity and Acceleration at the corresponding points in the model and at the corresponding points in the prototype are the same. Since velocity and Acceleration are vector quantities, hence not only the ratio of magnitude of velocity and acceleration at the corresponding points in model and prototype should be same ; but the directions of velocity and accelerations at the corresponding points in the model and prototype also should be parallel.
Let,
Vp1 = Velocity of fluid at point 1 in prototype,
Vp2 = Velocity of fluid at point 2 in prototype,
αρ1 = Acceleration of fluid at point 1 in prototype,
αρ2 = Acceleration of fluid at point 2 in prototype, and
Vm1, Vm2, αm1 ,αm2 = Corresponding values at the corresponding points of fluid velocity and acceleration in the model.
Also the directions of the velocities in the model and prototype should be same.
3:) Dynamic Similarity:
Dynamic similarity means the similarity of forces between the model and prototype. Thus dynamic similarity is said to exist between the model and the prototype if the ratios of the corresponding forces acting at the corresponding points are equal. Also the directions of the corresponding forces at the corresponding points should be same.
Let,
(fι)ρ = Inertia force at a point in prototype,
(fν)ρ = Viscous force at the point in prototype,
(fg)ρ = Gravity force at the point in prototype,
(fι)м, (fν)м, (fg)м = Corresponding values of forces at the corresponding point in model.
Then for dynamic similarity, we have
Also the direction of the corresponding forces at the corresponding points in the model and prototype should be same.
Credit:- Book Author- DR.R.K.Bansal
1. Geometric Similarity
2. Kinetic Similarity
3. Dynamic Similarity .
1:) Geometric similarity :
The Geometric similarity is said to exist between the model and the prototype. The ratio of all corresponding linear dimensions in the model and prototype are equal.
2:) Kinematic similarity :
Kinematic Similarity means the Similarity of motion between model and prototype. Thus kinematic similarity said to exist between the model and the prototype if the ratios of the velocity and Acceleration at the corresponding points in the model and at the corresponding points in the prototype are the same. Since velocity and Acceleration are vector quantities, hence not only the ratio of magnitude of velocity and acceleration at the corresponding points in model and prototype should be same ; but the directions of velocity and accelerations at the corresponding points in the model and prototype also should be parallel.
Let,
Vp1 = Velocity of fluid at point 1 in prototype,
Vp2 = Velocity of fluid at point 2 in prototype,
αρ1 = Acceleration of fluid at point 1 in prototype,
αρ2 = Acceleration of fluid at point 2 in prototype, and
Vm1, Vm2, αm1 ,αm2 = Corresponding values at the corresponding points of fluid velocity and acceleration in the model.
3:) Dynamic Similarity:
Dynamic similarity means the similarity of forces between the model and prototype. Thus dynamic similarity is said to exist between the model and the prototype if the ratios of the corresponding forces acting at the corresponding points are equal. Also the directions of the corresponding forces at the corresponding points should be same.
Let,
(fι)ρ = Inertia force at a point in prototype,
(fν)ρ = Viscous force at the point in prototype,
(fg)ρ = Gravity force at the point in prototype,
(fι)м, (fν)м, (fg)м = Corresponding values of forces at the corresponding point in model.
Then for dynamic similarity, we have
Credit:- Book Author- DR.R.K.Bansal
Comments
Post a Comment