A researcher suspects that the onset of turbulence in a fluid flowing through a long…
PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors
Problem
A researcher suspects that the onset of turbulence in a fluid flowing through a long straight pipe depends only on the following measurable quantities:
• Density of the fluid ρ
• Average speed of flow v
• Diameter of the pipe D
• Dynamic viscosity of the fluid η
(i) Assuming that the critical condition for turbulence can be expressed as Rc=ρavbDcηd, use dimensional analysis to determine the exponents a,b,c and d.
(ii) Write the simplest form of the resulting expression and identify the dimensionless constant that characterises the transition from laminar to turbulent flow in pipes.
(iii) Discuss briefly why this constant is useful in engineering practice, quoting a typical limiting value for water flowing in smooth pipes.