Viscosity is a measure of how strongly a fluid resists being sheared or made to flow. It matters in engineering because it controls pressure drop in pipes, lubrication between moving parts, mixing in tanks, and drag in channels. A Newtonian fluid is the simplest useful model because its shear stress is directly proportional to its shear rate.
Water, air, and many light oils behave approximately as Newtonian fluids under ordinary conditions.
Understanding Engineering: Viscosity and Newtonian Fluids
Viscosity comes from interactions inside a fluid. In a liquid, nearby molecules attract each other and continually exchange places. Moving one layer past another requires energy to overcome this internal friction.
In a gas, molecules travel between layers and carry momentum with them. This difference helps explain why liquids and gases respond differently to heating. A useful starting assumption in engineering is the no slip condition.
Fluid directly touching a stationary wall is stationary, while fluid beside a moving wall tends to move with that wall. The change in speed across the gap creates shearing.
The size of the gap matters greatly. Consider fluid trapped between two flat surfaces. If the same surface speed is applied across a smaller gap, the speed changes more sharply from one surface to the other.
More internal friction is produced, so more force is needed to keep the surface moving. The same idea appears in pipes. Fluid at the pipe wall moves very slowly, while fluid near the centre moves faster.
Viscosity transfers momentum between these regions. In smooth, slow flow, this produces an orderly velocity profile and a predictable energy loss along the pipe.
Engineers must balance viscosity against other needs. A thick lubricating oil can keep metal surfaces apart in a bearing, reducing wear. If it is too viscous, the machine wastes power stirring the oil and may struggle during a cold start.
In a pump or hydraulic system, a more viscous liquid can reduce leakage through small clearances. It can require more pumping power.
Food factories face similar choices when moving syrup, chocolate, or sauces through pipes. Viscosity affects how easily a tank mixes, how quickly bubbles rise, and whether a product can be filled into containers at a steady rate.
Temperature must be treated as part of every viscosity value. A number measured in a laboratory is incomplete unless the temperature is known. Engine oil that flows well in a warm engine can be much harder to move on a winter morning.
Air becomes more resistant to shear as it warms, which is less intuitive because many students expect every fluid to thin when heated. Another important limit is that not every fluid follows the Newtonian model. Paint may become easier to spread when stirred.
Toothpaste can behave like a solid until enough force is applied. Blood changes its flow behaviour with conditions.
When solving school problems, first identify whether the fluid can reasonably be treated as Newtonian, keep units consistent, and distinguish dynamic viscosity from kinematic viscosity. Density is needed when converting between them.
Key Facts
- Newtonian fluid law: tau = mu du/dy
- Shear rate between parallel plates: du/dy = U/h when the velocity profile is linear
- Shear stress for plate flow: tau = mu U/h
- Dynamic viscosity mu has SI units Pa s, which is the same as N s/m^2
- Kinematic viscosity: nu = mu/rho, with SI units m^2/s
- For most liquids, viscosity decreases as temperature increases, while for gases, viscosity usually increases as temperature increases
Vocabulary
- Dynamic viscosity
- Dynamic viscosity is the proportionality constant between shear stress and shear rate in a Newtonian fluid.
- Kinematic viscosity
- Kinematic viscosity is dynamic viscosity divided by density and describes how quickly momentum diffuses through a fluid.
- Shear stress
- Shear stress is the tangential force per unit area applied parallel to a fluid layer.
- Shear rate
- Shear rate is the change in fluid velocity with distance perpendicular to the flow direction.
- Newtonian fluid
- A Newtonian fluid is a fluid whose viscosity stays constant as shear rate changes at a fixed temperature and pressure.
Common Mistakes to Avoid
- Confusing dynamic viscosity and kinematic viscosity: dynamic viscosity measures resistance to shear, while kinematic viscosity equals mu/rho and includes the effect of density.
- Using tau = mu U instead of tau = mu U/h: the plate spacing matters because shear stress depends on the velocity gradient, not just the plate speed.
- Assuming every fluid is Newtonian: paints, blood, ketchup, and polymer solutions often change apparent viscosity with shear rate, so tau may not be proportional to du/dy.
- Ignoring temperature effects: viscosity values are temperature dependent, so calculations using tabulated data must match the fluid temperature.
Practice Questions
- 1 A 0.002 m thick layer of oil is between a fixed lower plate and a top plate moving at 0.60 m/s. If mu = 0.25 Pa s, find the shear rate and the shear stress on the plate.
- 2 A fluid has dynamic viscosity mu = 0.0012 Pa s and density rho = 850 kg/m^3. Calculate its kinematic viscosity in m^2/s.
- 3 Two fluids are tested in the same parallel-plate device at constant temperature. Fluid A gives a straight-line graph of shear stress versus shear rate through the origin, while Fluid B gives a curved graph. Explain which fluid is Newtonian and what the graph shape tells you about viscosity.