[2] To achieve kinematic similarity in a scaled model, dimensionless numbers in fluid dynamics come into consideration.
There are other dimensionless numbers that will also come into consideration, such as Womersley number[3] Assume we need to make a scaled up model of coronary artery with kinematic similarity.
To keep the Reynolds number the same, the scaled-up model can use a different fluid with different viscosity or density.
We can also change the velocity of the fluid to maintain the same dynamic characteristics.
The above equation can be written for artery as, Re (artery) = ρ1v1l1/μ1 = v1l1/ʋ1 And for the scaled-up model, Re (model) = ρ2v2l2/μ2 = v2l2/ʋ2 At the condition of Kinematic Similarity, Re (model) = Re (artery) That means, ρ1v1l1/μ1 = ρ2v2l2/μ2 or, v1l1/ʋ1 = v2l2/ʋ2 Substituting variables by provided values will provide important characteristics data for the fluid and flow characteristics for the scaled-up model.