Correct Answer - Option 4 : Length scale ratio, velocity scale ratio and force scale ratio
Explanation:
Similitude
- The similitude is defined as the similarity between the model and its prototype in every aspect.
- It means that the model and prototype have similar properties or model and prototype are completely similar.
Three types of similarities must exist between model and prototype.
-
Geometric similarity: the geometric similarity is said to exist between the model and prototype if the ratio of all corresponding linear dimensions in the model and prototype are equal.
\(\frac{{{L_p}}}{{{L_m}}} = \frac{{{D_p}}}{{{D_m}}} = {L_r}\)
where Lr is the scale ratio.
-
Kinematic similarity: the kinematic similarity is said to exist between the model and prototype if the ratios of velocity and acceleration at the corresponding points in the model and the corresponding points in the prototype are the same.
\(\frac{{{V_p}}}{{{V_m}}} = {V_r}\)
where Vr is the velocity ratio.
\(\frac{{{a_p}}}{{{a_m}}} = {a_r}\)
where ar is the acceleration ratio.
Note: Direction of velocities in the model and the prototype should also be the same.
-
Dynamic similarity: the dynamic similarity is said to exist between the model and prototype if the ratios of corresponding forces acting at the corresponding points are equal.
Also, the direction of corresponding forces at the corresponding points should be the same.
\(\frac{{{{\left( {{F_i}} \right)}_p}}}{{{{\left( {{F_i}} \right)}_m}}} = \frac{{{{\left( {{F_v}} \right)}_p}}}{{{{\left( {{F_v}} \right)}_m}}} = \frac{{{{\left( {{F_g}} \right)}_p}}}{{{{\left( {{F_g}} \right)}_m}}} \ldots = {F_r}\)
where Fr is the force ratio.
