PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
For liquid flow through a cylindrical pipe, the motion changes from laminar to turbulent when the speed exceeds a critical value vc. Suppose vc depends only on the liquid’s density ρ, coefficient of viscosity η, and the pipe radius r.
(i) Derive an expression for vc in terms of ρ,η and r, retaining an undetermined dimensionless constant.
(ii) From your result, write the dimensionless combination of ρ,vc,r and η that characterises the flow through the pipe.