Viscosity

### Viscosity

Viscosity is a measure of a fluid's resistance to deformation or flow. It is an essential property in fluid dynamics and determines how fluids behave under various conditions. The higher the viscosity, the more resistance the fluid has to flow. For example, honey has a higher viscosity than water.

There are two main types of viscosity: dynamic (or absolute) viscosity and kinematic viscosity. Dynamic viscosity is a measure of the internal friction within the fluid and is usually expressed in units of poise or Pascal-seconds (Pa·s). Kinematic viscosity, on the other hand, is the ratio of dynamic viscosity to the fluid's density and is measured in stokes (St).

### Key Concepts and Applications

1. **Measurement Instruments**: Rheometers are devices used to measure the viscosity of a fluid. They can provide information about how a fluid responds to applied shear stress.

2. **Newtonian and Non-Newtonian Fluids**: For Newtonian fluids, viscosity remains constant regardless of the shear rate (e.g., water, air). Non-Newtonian fluids, however, exhibit a viscosity that changes with the rate of shear (e.g., ketchup, blood).

3. **Temperature Dependence**: In general, the viscosity of liquids decreases with increasing temperature, while the viscosity of gases increases with temperature.

4. **Stokes' Law**: This law relates the drag force experienced by a spherical object moving through a fluid to the fluid's viscosity. The drag force is given by \( F = 6 \pi \eta r v \), where \( \eta \) is the dynamic viscosity, \( r \) is the radius of the sphere, and \( v \) is the velocity.

5. **Reynolds Number**: The Reynolds number (\( Re \)) is a dimensionless quantity that predicts flow patterns in different fluid flow situations. It is defined as \( Re = \frac{\rho vL}{\eta} \), where \( \rho \) is the fluid density, \( v \) is the flow velocity, \( L \) is a characteristic length, and \( \eta \) is the dynamic viscosity. Low Reynolds numbers indicate laminar flow, while high Reynolds numbers indicate turbulent flow.

6. **Viscosity in Polymers**: The viscosity of polymers can be described by models such as the Williams-Landel-Ferry (WLF) model, which accounts for temperature dependence.

### Clues Used Across Multiple Question Stems

1. **Resistance to Flow**:

   - "Describe a fluid’s resistance to flow."

   - "Measure of a fluid’s resistance to flow."

   - "Fluid’s resistance to deformation or flow."

2. **Units of Measurement**:

   - "Measured in units of poise or stokes."

   - "Dynamic variety is measured in poise, while kinematic variety is measured in stokes."

3. **Relation to Other Properties**:

   - "Appears in the denominator of the Reynolds number."

   - "Dividing dynamic viscosity by density gives kinematic viscosity."

### Related Quizbowl Facts That Appeared In More Than One Toss-up on qbreader.org

1. The Reynolds number (\( Re \)) is the ratio of inertial forces to ___1___ forces in a fluid.

2. ___2___ fluids have a constant viscosity regardless of the shear rate.

3. The viscosity of a fluid can be measured using instruments such as ___3___.

4. In ___4___' law, the drag force on a sphere is proportional to the fluid’s _viscosity.

5. The ___5___number is the ratio of momentum diffusivity to thermal diffusivity, where momentum diffusivity is equivalent to viscous diffusivity.

6. ___6___’s formula relates the viscosity of an ideal gas to its temperature.

Answers:

1. Viscous

2. Newtonian

3. Rheometers

4. Stokes

5. Prandtl

6. Sutherland

1. **Prandtl number** - 11 occurrences

2. **Newtonian fluids** - 10 occurrences

3. **Reynolds number** - 9 occurrences

4. **Thixotropic materials/behavior** - 9 occurrences

5. **Superfluids (having zero viscosity)** - 8 occurrences

6. **Stokes law/formula** - 7 occurrences

7. **Kinematic and dynamic viscosity** - 7 occurrences

8. **Resistance to flow** - 6 occurrences

9. **Poise (as a unit of viscosity)** - 5 occurrences

10. **Navier-Stokes equations** - 5 occurrences

11. **Boundary layer (Prandtl)** - 4 occurrences

12. **Sutherland’s formula** - 4 occurrences

13. **Viscosity measurement devices (Zahn cup, etc.)** - 4 occurrences

14. **Grashof number** - 3 occurrences

**Prandtl number**: A dimensionless number that characterizes the relative thickness of the momentum and thermal boundary layers in fluid flow. It is the ratio of kinematic viscosity to thermal diffusivity.

**Newtonian fluids**: Fluids that have a constant viscosity independent of the shear rate. Examples include water and air.

**Reynolds number**: A dimensionless number that predicts the flow regime in a fluid, such as laminar or turbulent flow. It is the ratio of inertial forces to viscous forces.

**Thixotropic materials/behavior**: Fluids that decrease in viscosity over time when subjected to shear stress and recover their viscosity when the stress is removed.

**Superfluids (having zero viscosity)**: Fluids that can flow without viscosity, allowing them to move through narrow channels without losing kinetic energy. Examples include liquid helium at very low temperatures.

**Stokes law/formula**: A mathematical equation that describes the force of viscosity on a spherical object moving through a fluid. It is used to calculate the terminal velocity of small particles in a fluid.

**Kinematic and dynamic viscosity**: Kinematic viscosity is the ratio of dynamic viscosity to fluid density, while dynamic viscosity measures a fluid's internal resistance to flow.

**Resistance to flow**: The opposition a fluid offers to flow due to internal friction, often described by its viscosity.

**Poise (as a unit of viscosity)**: A unit of dynamic viscosity in the centimeter-gram-second (CGS) system. One poise equals one dyne-second per square centimeter.

**Navier-Stokes equations**: A set of partial differential equations that describe the motion of viscous fluid substances. They are fundamental to fluid mechanics and describe how the velocity field of a fluid evolves over time.

**Boundary layer (Prandtl)**: The thin layer of fluid near a solid boundary where the fluid velocity changes from zero (at the wall) to the free stream value. Ludwig Prandtl developed the concept, which is crucial for understanding drag and heat transfer.

**Sutherland’s formula**: An empirical relationship that describes the variation of the viscosity of a gas with temperature.

**Viscosity measurement devices (Zahn cup, etc.)**: Instruments used to measure the viscosity of fluids, such as the Zahn cup, viscometers, and rheometers.

**Grashof number**: A dimensionless number that estimates the ratio of buoyancy to viscous forces in a fluid. It is used in the study of natural convection.

These terms collectively describe key concepts and properties in the study of fluid dynamics, particularly concerning viscosity, flow regimes, and the equations governing fluid motion. They are essential for understanding how fluids behave in various engineering and scientific applications.