Viscosity and Flow Regimes

Laminar and turbulent flow regimes, Poiseuille's law, and Reynolds number in closed conduits.

General idea of the topic

Viscosity is the internal resistance of a fluid to one layer sliding over another. It explains why honey flows more slowly than water and why in a pipe the velocity is maximum at the center and zero at the wall.

The topic defines viscosity, distinguishes laminar flow, ordered in layers, from turbulent flow, with eddies, and presents the Reynolds number, which predicts the regime. It ends with head loss, the energy the flow loses to friction along a pipe.

What you will truly understand

By the end you will be able to compute the Reynolds number, decide whether a flow is laminar or turbulent and estimate the pressure drop in a pipe.

You will also know why laminar flow needs less energy than turbulent flow for the same flow rate.

Recommended learning route

1. Viscosity: shear stress, velocity gradient and units of dynamic and kinematic viscosity.
2. Laminar Flow: layered flow and the parabolic velocity profile in a pipe.
3. Turbulent Flow: flow with eddies, mixing and greater friction.
4. Reynolds Number: ratio of inertial to viscous forces and critical transition values.
5. Head Loss: energy lost to friction and its calculation in pipes.

Physical criterion you must acquire

The essential criterion is to compute Re = ρvD/μ with the right quantities and compare it with the threshold of the geometry. In a circular pipe, Re below about 2000 indicates laminar flow and above about 4000, turbulent; in between there is transition and no reliable prediction.

Connection with real problems

• water, oil and gas pipelines.
• lubrication and oils.
• blood circulation.
• aerodynamics and drag on vehicles.

Final goal of the topic

The final goal is to characterize the regime of a flow and estimate viscous losses in real systems.