An incompressible Newtonian fluid flows in a pipe of diameter $D_{1}$ at volumetric flow rate $Q$.  Fluid with same properties flows in another pipe of diameter $D_{2}=D_{1}/2$ at the same flow rate $Q$ . The transition length required for achieving fully-developed flow is $l_{1}$ for the tube of diameter $D_{1}$, while it is $l_{2}$ for the tube of diameter $D_{2}$. Assuming steady laminar flow in both cases, the ratio $l_{1}/l_{2}$ is:

1. $1/4$
2. $1$
3. $2$
4. $4$