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The velocity of sphere formula calculates the mean velocity of a spherical object moving through a fluid when the resistance force, dynamic viscosity, and sphere diameter are known. This equation is derived from Stokes' law for fluid resistance on spherical surfaces.
The calculator uses the formula:
Where:
Explanation: This formula describes the relationship between the resistance force experienced by a sphere moving through a viscous fluid and its resulting velocity.
Details: Calculating the mean velocity of a sphere in a fluid is crucial for understanding fluid dynamics, designing particle separation systems, analyzing sedimentation processes, and studying rheological properties of fluids.
Tips: Enter resistance force in newtons, dynamic viscosity in pascal-seconds, and sphere diameter in meters. All values must be positive and greater than zero.
Q1: What assumptions does this formula make?
A: This formula assumes laminar flow, spherical particles, and that the fluid is Newtonian and infinite in extent.
Q2: When is this formula applicable?
A: This formula is valid for low Reynolds numbers (Re < 1) where Stokes' law applies, typically for small particles in viscous fluids.
Q3: What are typical values for dynamic viscosity?
A: Water at 20°C has μ ≈ 0.001 Pa·s, while honey has μ ≈ 10 Pa·s, and air has μ ≈ 0.000018 Pa·s.
Q4: How does sphere diameter affect velocity?
A: Velocity is inversely proportional to sphere diameter - smaller spheres experience higher velocities for the same resistance force.
Q5: What are the limitations of this equation?
A: The equation becomes less accurate for non-spherical particles, at higher Reynolds numbers, or when wall effects are significant.