Laminar and Turbulent Flow in Pipes and Ducts

For pipe flow applications, it's often important to be able to determine whether a given flow condition is laminar flow or turbulent flow. Different equations or methods of analysis often apply to laminar flow and turbulent flow conditions.

The concepts of laminar and turbulent flow are shown in the diagram in the next section. Laminar flow (also called streamline flow or viscous flow) occurs with relatively slow velocity, high viscosity flows, and is characterized by all of the fluid velocity vectors lined up in the direction of flow. Turbulent flow, on the other hand occurs with relatively high velocity, low viscosity flows, and has point velocity vectors in all directions, although the overall flow is in one direction, along the axis of the pipe.

Practical transport of water or air in a pipe or other closed conduit is typically turbulent flow. Similarly, flow of other gases or liquids with viscosity similar to water will normally be transported in conduits under turbulent flow conditions. Laminar flow would often be present with liquids of high viscosity, such as lubricating oils.

The typical criterion for whether pipe flow is laminar or turbulent is the value of the Reynold's Number. The Reynold's number for pipe flow is defined as Re = DVρ/μ, where D is the pipe diameter, V is the average velocity in the pipe, ρ is the density of the flowing fluid and μ is the dynamic viscosity of the flowing fluid. Re is a dimensionless number. Any consistent set of units can be used for D, V, ρ and μ, and will result in Re being dimensionless. The generally accepted criteria for laminar and turbulent flow in terms of Re are as follows:

For Re < 2100, the flow is laminar

For Re > 4000, the flow is turbulent

For 2100 < Re < 4000, the flow is in the transition region

For flow in the transition region, the flow may be either laminar or turbulent, depending upon the nature of the entrance to the pipe and the pipe wall roughness.

Fluids also flow through non-circular, closed conduits, such as HVAC ducts or heat exchangers. In that case the definition of the Reynold's Number becomes: Re = 4R_HVρ/μ. Note that pipe diameter, D, has been replaced with 4R_H, where R_H is the hydralic radius, defined as: R_H = A/P = cross-sectional area normal to flow/wetted perimeter. For example, the hydraulic radius for a 6" by 12" rectangular furnace duct would be: R_H = (0.5)(1)/[(2)(0.5) + (2)(1)] = 0.5/3 = 0.167 ft

Consider flow of 1.2 cfs of water at 50^oF through a 4" diameter pipe. What is the Reynold's Number for this flow? Is it laminar or turbulent flow?

Solution: Values for the density and viscosity of water at 50^oC are needed. Such values are available in fluid mechanics or thermodynamics textbooks, handbooks and on the internet. The values needed for this problem are: ρ = 1.94 slugs/ft³ and μ = 2.34 x 10^-5 lb-sec/ft². The velocity, V, can be calculated from V = Q/A = Q/(πD²/4) = 1.2/[π(1/3)²/4] = 1.34 ft/sec. Substituting values into Re = DVρ/μ gives Re = (1/3)(1.34)(1.94)/2.34 x 10^-5, or Re = 3.70 x 10⁴. This value of Re is greater than 4000, so this is turbulent flow.