Summarizing Viscosity and Laminar Flow

Summary

• Laminar flow is characterized by smooth flow of the fluid in layers that do not mix.
• Turbulence is characterized by eddies and swirls that mix layers of fluid together.
• Fluid viscosity \(\eta \) is due to friction within a fluid. Representative values are given in this table. Viscosity has units of \(({\text{N/m}}^{2})\text{s}\) or \(\text{Pa}\cdot \text{s}\).
• Flow is proportional to pressure difference and inversely proportional to resistance:

  \(Q=\cfrac{{P}_{2}-{P}_{1}}{R}.\)

• For laminar flow in a tube, Poiseuille’s law for resistance states that

  \(R=\cfrac{8\eta l}{{\mathrm{\pi r}}^{4}}.\)

• Poiseuille’s law for flow in a tube is

  \(Q=\cfrac{({P}_{2}-{P}_{1})\pi {r}^{4}}{8\eta l}.\)

• The pressure drop caused by flow and resistance is given by

  \({P}_{2}-{P}_{1}=RQ.\)

Glossary

laminar

a type of fluid flow in which layers do not mix

turbulence

fluid flow in which layers mix together via eddies and swirls

viscosity

the friction in a fluid, defined in terms of the friction between layers

Poiseuille’s law for resistance

the resistance to laminar flow of an incompressible fluid in a tube: R = 8ηl/πr⁴

Poiseuille’s law

the rate of laminar flow of an incompressible fluid in a tube: Q = (P₂ − P₁)πr⁴/8ηl