Answer
constant $ \frac{\pi }{8}$ is dimensionless and yes this equation classify as homogeneous equation
Work Step by Step
$Q=\frac{\pi R^{4} \Delta P}{8 \mu \iota}$ we put dimensions in equation as follows : $Q =L^{3} T^{-1} $ & R = L & $\mu = F L^{-2}T$ & $\Delta P = M L^{-1} T^{-2}$ & $ \iota =L $
$ L^{3} T^{-1} = \frac{\pi}{8} \times \frac{L^{4}\times M L^{-1} T^{-2} }{F L^{-2}T \times L}$ where $F =M L^{-1} T^{-2}$
Delete similar dimensions , $\frac{\pi}{8}$ become dimensionless
