Viscosity is like a way to measure how easy or hard it is for a liquid to let things move through it. If a liquid has low viscosity, we say it’s “thin,” and if it has high viscosity, we say it’s “thick.” Moving through something like water is easier because it has low viscosity, but moving through something like honey is harder because it has high viscosity.
Daily Life Examples
- Pouring water (low viscosity) is easier than pouring honey (high viscosity).
- Ketchup (around 50,000 cP) flows slowly due to its high viscosity.
- Motor oil (around 100 cP) has higher viscosity than gasoline (around 0.5 cP).
- Pancake syrup (around 1500 cP) is thicker and more viscous than water.
- Shampoo (around 1000 cP) has moderate viscosity, making it flow smoothly.
- Honey (around 10,000 cP) is much more viscous than olive oil (around 80 cP).
- Blood (around 4.5 cP) has lower viscosity than honey but higher than water.
Mathematical Form and Unit
The mathematical formula for viscosity (η) is defined as the ratio of shear stress (τ) to shear rate (γ˙). Mathematically, it is expressed as:
η=τγ˙
Where:
- η is the viscosity measured in units of Pa⋅s (Pascal-seconds) or N⋅s/m2 (Newton-seconds per square meter),
- τ is the shear stress measured in units of Pa (Pascals) or N/m2(Newtons per square meter),
- γ˙ is the shear rate measured in units of s−1 (inverse seconds).
Solved Example
A fluid experiences a shear stress (τ) of 20 Pascals when a shear rate (γ˙) of 5 s−1 is applied. Calculate the viscosity (η) of the fluid.
Solution: The formula for viscosity (η) is given by:
η=τγ˙
Substitute the given values:
η=20 Pa/5 s−1 = 4 Pa⋅s
Newtonian and Non-Newtonian Fluid Viscosity
In Newtonian fluids, like water or air, viscosity remains constant, providing a proportional increase in resistance as force is applied. Newtonian fluids maintain fluid-like behavior regardless of force.
Conversely, non-Newtonian fluids, such as Oobleck or magnetorheological fluids, exhibit varying viscosity based on applied force. Oobleck shows solid-like behavior under significant force, while magnetorheological fluids transition from nearly solid to fluid in response to magnetic fields. Non-Newtonian fluids deviate from constant viscosity, showcasing diverse behaviors under different forces or conditions.
Crux Points
- Viscosity: Measure of a fluid’s resistance to flow.
- Unit: Expressed in Pascals seconds (Pa·s) or Newton-seconds per square meter (N·s/m²).
- Examples: Water (Newtonian), ketchup (Shear-thinning, non-Newtonian), toothpaste (Bingham plastic, non-Newtonian).
- Newtonian Fluids: Constant viscosity, like water and air.
- Non-Newtonian Fluids: Varying viscosity, e.g., Oobleck (Shear-thinning) and toothpaste (Bingham plastic).
