Final answer:
The Reynolds number determines when viscous effects are important, with flows having a Re < 1 being fully viscous. Wind speed at which Re falls below 1 would be lower for smaller objects like a twig or hair and higher, yet still low, for large objects like a smokestack.
Step-by-step explanation:
The question relates to the concept of viscous flow and the determination of when viscous effects are important in a fluid flow situation. The key parameter to consider is the Reynolds number (Re), a dimensionless number used in fluid mechanics to characterize the flow regime, especially the transition between laminar and turbulent flow. Reynolds number is defined as Re = (ρvD)/μ, where ρ is the fluid density, v is the flow velocity, D is the characteristic diameter, and μ is the dynamic viscosity. For flow to be considered laminar and thus for viscous effects to be important throughout the entire flow field, Re must be less than 1. Due to the complexity of this calculation without additional data such as the air density and viscosity, this calculation is better suited for a textbook or simulation that contains tables or equations for these properties.
Given the diameters mentioned (0.25 in. for the twig, 0.004 in. for the hair, and 6 ft. for the smokestack), under typical atmospheric conditions, the wind speed at which Re will be less than 1 would be significantly lower for smaller diameters. This is because a smaller diameter at a fixed fluid density and viscosity results in a lower Reynolds number for the same velocity. Thus, for the twig and hair, the wind speed must be very low for viscous effects to dominate, while for the smokestack, this critical speed might be higher, yet still relatively low in practical scenarios.