Shear Rate Calculator
What is Shear Rate?
Shear rate, often denoted by $\dot{\gamma}$, is a fundamental concept in rheology, the study of the flow of matter. It quantifies how quickly the fluid layers are sliding past one another. In simpler terms, it measures the rate at which deformation occurs within a fluid due to applied stress.
The units of shear rate are typically inverse seconds ($s^{-1}$). A higher shear rate means the fluid is undergoing deformation more rapidly.
How is Shear Rate Calculated?
The shear rate can be calculated using the following formula, which relates the velocity gradient across the fluid to a geometric shape factor:
$$ \dot{\gamma} = \gamma \frac{dv}{dy} $$
- $\dot{\gamma}$ is the Shear Rate (in $s^{-1}$).
- $\gamma$ is the Shape Factor, which depends on the geometry of the flow. For example, for flow between parallel plates, it is often approximated as 1. For flow in a capillary tube, it is related to the radius and the velocity at the wall.
- $\frac{dv}{dy}$ is the Velocity Gradient, which represents the change in velocity ($dv$) across a perpendicular distance ($dy$) within the fluid. This is typically measured in units of velocity per distance (e.g., m/s per m, or $s^{-1}$).
Example Calculation:
Consider a fluid flowing between two parallel plates. The top plate is moving at a certain velocity, and the bottom plate is stationary. If the distance between the plates is small, the velocity profile can be approximated as linear, and the velocity gradient ($\frac{dv}{dy}$) is constant.
Let's assume:
- Velocity Gradient ($\frac{dv}{dy}$) = 150 $s^{-1}$
- Shape Factor ($\gamma$) = 1.0 (for the parallel plate approximation)
Using the formula:
Shear Rate ($\dot{\gamma}$) = 1.0 * 150 $s^{-1}$ = 150 $s^{-1}$
In this scenario, the shear rate is 150 inverse seconds. This value is crucial for understanding how the fluid will behave under these flow conditions, including its viscosity and flow resistance.