Final answer:
The flow of oil with a kinematic viscosity of 0.5 Stokes in a pipe of diameter 7.5 cm becomes turbulent at a critical velocity of 2.875 m/s, as indicated by a Reynolds number well above the typical critical threshold of 2000-2400.
Step-by-step explanation:
The student's question is about determining when the flow of an oil with a kinematic viscosity of 0.5 Stokes through a pipe of diameter 7.5 cm becomes critical. The flow is considered critical when it transitions from laminar to turbulent, which is often assessed using the Reynolds number. In this context, the critical velocity is given as 2.875 m/s. Whether this velocity represents the onset of turbulence can be verified by calculating the Reynolds number and comparing it to the critical Reynolds number for flow in a pipe, which is typically around 2000-2400. The kinematic viscosity in units commonly used for this calculation is 0.5 Stokes or 0.5 x 10-4 m2/s. Hence, with the provided velocity and pipe diameter, the Reynolds number would be:
Re = (velocity) × (pipe diameter) / (kinematic viscosity)
Re = (2.875 m/s) × (0.075 m) / (0.5 x 10-4 m2/s) = 43125
This calculation shows that the flow is well above the critical Reynolds number and therefore it would be turbulent, not laminar, assuming typical flow conditions.