Buckingham Pi Theorem
This example is the same as example 7.2 in the textbook except that we assume the pipe is a smooth pipe. Using Buckingham Pi theorem, determine the dimensionless P parameters involved in the problem of determining pressure drop along a straight horizontal circular pipe.
- Relevant flow parameters: Dp pressure drop, r density, V averaged velocity, m viscosity, L pipe length, D pipe diameter. Therefore the pressure drop is a function of five variables. Dp=f1(r,V, m, L, D) See step 1 p. 300
Buckingham theorem states that the total number of these relevant dimensional parameters (n) can be grouped into n-m independent dimensionless groups. The number m is usually equal to the minimum of independent dimensions required to specify the dimensions of all relevant parameters.