How does viscosity affect Reynolds number and the transition between laminar and turbulent flow?

• A. Higher viscosity lowers Reynolds number, promoting laminar flow; lower viscosity raises Reynolds number, promoting turbulence.
• B. Viscosity does not affect Reynolds number.
• C. Higher viscosity increases Reynolds number, promoting turbulence.
• D. Lower viscosity always yields laminar flow regardless of velocity.

Answer: (A)

Reynolds number measures the balance between inertial forces and viscous forces in a flow. It can be written as Re = ρ v L / μ (or Re = vL/ν, with ν = μ/ρ). Because viscosity μ sits in the denominator, increasing viscosity makes viscous forces stronger and Re smaller; this dampens disturbances and tends to keep the flow smooth and laminar. Decreasing viscosity lowers viscous resistance, raises Re, and makes it easier for disturbances to grow into turbulence once a critical value is reached. The exact threshold depends on geometry and conditions, but in many pipe flows the transition from laminar to turbulent occurs as Re climbs into the thousands.