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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. $4$
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