1. What is Velocity Gradient?

The Velocity Gradient refers to the difference in velocity between the adjacent layers of the fluid. It is a crucial parameter in fluid dynamics that helps determine the rate of shear in fluid flow, particularly important in viscosity measurements.

2. How Does the Calculator Work?

The calculator uses the Velocity Gradient formula:

Where:

• \( VG \) — Velocity Gradient (m/s)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( r_2 \) — Radius of Outer Cylinder (m)
• \( \Omega \) — Angular Speed (rad/s)
• \( r_1 \) — Radius of Inner Cylinder (m)

Explanation: This formula calculates the velocity gradient between two concentric cylinders, where the outer cylinder rotates with a specific angular speed, creating a shear flow in the fluid between them.

3. Importance of Velocity Gradient Calculation

Details: Velocity gradient is essential for determining fluid viscosity, analyzing shear stress in fluid flows, and understanding fluid behavior in various engineering applications, particularly in rheology and fluid mechanics.

4. Using the Calculator

Tips: Enter the radius of outer cylinder and inner cylinder in meters, angular speed in rad/s. Ensure the outer cylinder radius is greater than the inner cylinder radius. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of velocity gradient?
A: Velocity gradient represents the rate of change of velocity with respect to distance perpendicular to the flow direction, indicating the shear rate in the fluid.

Q2: How is velocity gradient related to viscosity?
A: According to Newton's law of viscosity, shear stress is directly proportional to the velocity gradient, with viscosity being the constant of proportionality.

Q3: What are typical units for velocity gradient?
A: Velocity gradient is typically measured in meters per second per meter (m/s/m), which simplifies to per second (s⁻¹).

Q4: When is this formula particularly useful?
A: This formula is especially useful in concentric cylinder viscometers where the outer cylinder rotates and the inner cylinder remains stationary.

Q5: Are there limitations to this calculation?
A: This calculation assumes laminar flow, Newtonian fluid behavior, and no end effects in the cylindrical geometry.