Viscosity is a measure of how strongly a fluid resists flowing, and it affects everything from blood moving through arteries to oil moving through an engine. In a viscous fluid, neighboring layers drag on each other, so motion is not the same everywhere in the fluid. Laminar flow is the smooth, orderly flow pattern that occurs when these layers slide past one another without chaotic mixing.
Understanding laminar flow helps engineers design pipes, medical devices, lubrication systems, and microfluidic channels.
Key Facts
- Viscosity measures internal resistance to flow, with dynamic viscosity symbol η and SI unit Pa s.
- For a Newtonian fluid, shear stress is proportional to velocity gradient: τ = η dv/dy.
- In laminar pipe flow, fluid speed is zero at the wall and maximum at the center.
- The velocity profile in a circular pipe is parabolic: v(r) = vmax(1 - r^2/R^2).
- The Reynolds number predicts flow type: Re = ρvD/η.
- For laminar flow in a circular pipe, volume flow rate follows Poiseuille's law: Q = πΔP R^4/(8ηL).
Vocabulary
- Viscosity
- Viscosity is a fluid property that describes how much the fluid resists being deformed or made to flow.
- Laminar flow
- Laminar flow is smooth fluid motion in which layers move in orderly paths with little mixing between layers.
- Turbulent flow
- Turbulent flow is irregular fluid motion with swirling eddies, strong mixing, and rapidly changing velocities.
- Velocity profile
- A velocity profile shows how fluid speed changes across a pipe, channel, or boundary layer.
- Reynolds number
- The Reynolds number is a dimensionless ratio that compares inertial effects to viscous effects in a flowing fluid.
Common Mistakes to Avoid
- Assuming all points in a pipe have the same speed is wrong because viscosity and the no-slip condition make the fluid slowest at the wall and fastest at the center.
- Forgetting the no-slip condition is wrong because real fluids in contact with a solid surface have zero speed relative to that surface.
- Treating high viscosity as the same as high density is wrong because viscosity measures resistance to flow while density measures mass per unit volume.
- Using Poiseuille's law for turbulent flow is wrong because Q = πΔP R^4/(8ηL) applies only to steady laminar flow of a Newtonian fluid in a circular pipe.
Practice Questions
- 1 Water flows through a pipe with average speed 0.50 m/s, diameter 0.020 m, density 1000 kg/m^3, and viscosity 1.0 x 10^-3 Pa s. Calculate the Reynolds number and decide whether the flow is likely laminar or turbulent.
- 2 Oil with viscosity 0.20 Pa s flows through a circular tube of radius 0.0050 m and length 1.0 m under a pressure difference of 800 Pa. Use Q = πΔP R^4/(8ηL) to find the volume flow rate.
- 3 Explain why the velocity profile in laminar pipe flow is parabolic instead of flat, using viscosity and the no-slip condition in your answer.