= Solution
Use the pipe-diameter convention for the <Reynolds number>, with mean <velocity> $\bar v$, <density> $\rho$ and <dynamic viscosity> $\mu$:
$$
\mathrm{Re}=\frac{\rho\bar vD}{\mu},\qquad
D_{\rm crit}=\frac{\mathrm{Re}_{\rm crit}\mu}{\rho\bar v}.
$$
The <Reynolds number> compares inertial and viscous effects in the <fluid flow>. A conventional estimate for the onset of <turbulence> in a pipe is $\mathrm{Re}_{\rm crit}\simeq2000$, giving
$$
D_{\rm crit}=\frac{2000(3.16\times10^{-4}\,\mathrm{Pa\,s})}{(789\,\mathrm{kg\,m^{-3}})(0.5\,\mathrm{m\,s^{-1}})}=1.60\times10^{-3}\,\mathrm m.
$$
Hence the usual onset estimate is $\boxed{D\gtrsim1.6\,\mathrm{mm}}$. Using the also common transition criterion $\mathrm{Re}_{\rm crit}=2300$ gives $1.84\,\mathrm{mm}$, whereas $\mathrm{Re}\gtrsim4000$, used for established <turbulence>, gives $D\gtrsim3.2\,\mathrm{mm}$. There is no universal sharp minimum: inlet disturbances and pipe conditions affect the transition from <laminar flow>, so the threshold convention must accompany the answer.
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