Water flows steadily, fully developed and laminar through a smooth circular pipe of diameter 10 cm and length 10 m. Pressure drop is 0.2 Pa; kinematic viscosity $10^{-6}$ m²/s and density 1000 kg/m³. Find centerline velocity (one decimal mm/s).
Dynamic viscosity is $\mu=\rho\nu=0.001$ Pa·s. Poiseuille flow has $u_{max}=\Delta p R^2/(4\mu L)=0.2(0.05)^2/[4(0.001)(10)]=0.0125$ m/s. Thus **12.5 mm/s**. The mean is half that value, giving Reynolds number 625, consistent with laminar flow.
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