= Solution
The <Reynolds number> is $\mathrm{Re}=\rho UL/\eta=UL/\nu$, comparing inertial <stress> $\rho U^2$ with viscous <stress> $\eta U/L$. Nondimensionalizing an incompressible Newtonian <flow> with <velocity> $U$, <length> $L$ and <pressure> $\rho U^2$ gives
$$
\partial_{t^*}\mathbf v^*+\mathbf v^*\cdot\nabla^*\mathbf v^*
=-\nabla^*p^*+\frac1{\mathrm{Re}}\nabla^{*2}\mathbf v^*.
$$
At small <Reynolds number> inertia is negligible and a creeping-flow balance applies. At large <Reynolds number> the outer <flow> may be approximately inviscid, but thin no-slip <boundary layers> can still govern drag, separation and dissipation. A high <Reynolds number> permits turbulent motion without guaranteeing it; transition depends on geometry, disturbances and roughness.
Dynamically similar model experiments need matching geometry and relevant dimensionless parameters, including <Reynolds number>. If gravity, compressibility or surface tension matters, Froude, Mach or capillary-related parameters must also be matched. Testing linear pressure-flow or force-speed relations while varying $U$, $L$, <viscosity> and <temperature> is more informative than assigning one universal transition value to all apparatus.
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