Mumbai University > Civil Engineering > Sem 5 > Applied Hydraulics 1

Marks: 10M

Year: Dec 2014

The Rayleigh's method of dimensional analysis becomes more laborious if the variables are more than the number of fundamental dimensions (M, L, t). This difficulty is overcame by using Buckingham's Pi - theorem, which states, "If there are n variables (independent and dependent vcariables) in a physical phenomenon and if these variables contain m fundamental dimensions (M, L, T) then the variables are arranged into (n - m) dimensional terms. Each term is called as Pi-terms."

Following are the rules for repeating variables":-

1. As far as possible, the dependent variable should not be selected as repeating variables.

2. The repeating variables should be chhosen in such a way that one variable contains fluid property.

   • Variables with geometric property are

     (i) length (l) (ii) d (iii) Height, H etc.

   • variables with flow property are

     (i) Velocity, V (ii) Acceleration etc.

   • Variables with fluid property

     (i) $\mu$ (ii) $\rho$ (iii) $\omega$ etc.

3. The repeating variables selected should not form a dimensional group.

4. The repeating variable together must have the same number of fundamental dimension.

5. No two repeating variables should have the same dimension