You are helping a medical device company design a new type of personalised stent and need to design a series of experiments in order to test it. You consider the blood velocity, viscosity, density, diameter of the blood vessel and gravitational acceleration as relevant physical parameters. How many non-dimensional numbers define this problem? Work in SI units.Group of answer choices14None of the available options32
Question
You are helping a medical device company design a new type of personalised stent and need to design a series of experiments in order to test it. You consider the blood velocity, viscosity, density, diameter of the blood vessel and gravitational acceleration as relevant physical parameters. How many non-dimensional numbers define this problem? Work in SI units.Group of answer choices14None of the available options32
Solution
The Buckingham Pi theorem is a key principle in dimensional analysis, and it's used to determine the number of dimensionless parameters (or Pi terms) in a physical problem.
The theorem states that the number of dimensionless parameters is equal to the total number of variables in the problem minus the number of fundamental dimensions.
In this case, the total number of variables is 5 (blood velocity, viscosity, density, diameter of the blood vessel, and gravitational acceleration).
The number of fundamental dimensions is 3 (Mass, Length, and Time, as we're working in SI units).
So, according to the Buckingham Pi theorem, the number of dimensionless parameters is 5 - 3 = 2.
Therefore, two non-dimensional numbers define this problem.
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