Consider steady flow of an incompressible fluid through two long and straight pipes of diameters $d_{1}$ and $d_{2}$ arranged in series. Both pipes are of equal length and the flow is turbulent in both pipes. The friction factor for turbulent flow though pipes is of the form, $f=K(Re)^{-n}$, where $K$ and $n$ are known positive constants and $Re$ is the Reynolds number. Neglecting minor losses, the ratio of the frictional pressure drop in pipe $1$ to that in pipe $2$, $\left ( \dfrac{\Delta P_{1}}{\Delta P_{2}} \right )$, is given by

- $\left ( \dfrac{d_{2}}{d_{1}} \right )^{(5-n)} \\$
- $\left ( \dfrac{d_{2}}{d_{1}} \right )^{5} \\$
- $\left ( \dfrac{d_{2}}{d_{1}} \right )^{(3-n)} \\$
- $\left ( \dfrac{d_{2}}{d_{1}} \right )^{(5+n)}$