Chapter 1 - Introduction and Mathematical Concepts - Problems - Page 24: 60

n = 4

Here we use the dimensional analysis to find the value of n. (Symbol $\pi$ & the number 8 have no dimensions) $Q=\frac{\pi R^{n}(P_{1}-P_{2})}{8\eta L}$ $\frac{[L]^{3}}{[T]}=\frac{[L]^{n}\frac{[M]}{[L][T]^{2}}}{\frac{[M]}{[L][T]}[L]}=\frac{[L]^{n}[T]}{[L][T]^{2}}=\frac{[L]^{n}}{[L][T]}$ $[L]^{3}=[L]^{n-1}=\gt [L]^{4}=[L]^{n}$ So, we find that n = 4