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Water flows out of a circular tap of radius 0.5 cm. Determine how the nature of the flow changes when the flow rate is increased from 0.18 L/min to 0.48 L/min. (Viscosity of water = 10⁻³ Pa.s, density of water = 10³ kg/m³.) Classify using the Reynolds number (steady/laminar below the lower critical value, unsteady/turbulent above the upper critical value).

1. Steady flow to unsteady flow
2. Unsteady to steady flow
3. Remains steady flow
4. Remains turbulent flow

Correct answer: Steady flow to unsteady flow

Solution

Convert: Q1 = 0.18 L/min = 3e-6 m³/s, Q2 = 0.48 L/min = 8e-6 m³/s. Using Re = 2 rho Q/(pi r eta) (equivalently rho v D/eta with D = 2r), the larger flow rate gives a substantially larger Reynolds number that crosses the critical value, while the smaller one stays in the steady range. As Q increases, Re rises past the critical value, so flow changes from steady (laminar) to unsteady (turbulent).

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