Using Buckingham's $\pi$ obtain expression $\Delta P$.

Solution:

$\Delta P$ is a function of $D,l,V,$ $\mu$,$\rho ,K$,

$\Delta P$=$f(D,l,V,\mu,\rho,k)$.....(1)

Total variables n=7

writing dimensions of each variable,

Dimension of $\Delta P$=Dimension of pressure

=$ML^{-1}T^{-2}$

D=L, l=L, $VLT^{-1}$

$\mu=ML^{-1}T^{-1}$

$\rho=ML^{-3}$

K=L

Number of fundamental dimensions M=3

No of $\pi$ terms …