Total Drag Force On Sphere Calculator

Total Drag Force on Sphere Formula:

\[ F_D = 3 \times \pi \times \mu_d \times D \times v \]

Dynamic Viscosity of Fluid (μd):

Pa·s

Diameter of Sphere in Fluid (D):

Velocity of Body or Fluid (v):

m/s

Total Drag Force on Sphere (F_D):

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1. What is Total Drag Force on Sphere?

The Total Drag Force on a Sphere in fluid flow is the combined force acting on the sphere due to pressure drag and skin friction drag. It represents the resistance experienced by the sphere as it moves through a fluid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_D = 3 \times \pi \times \mu_d \times D \times v \]

Where:

\( F_D \) — Total Drag Force on Sphere (N)
\( \pi \) — Archimedes' constant (≈3.14159)
\( \mu_d \) — Dynamic Viscosity of Fluid (Pa·s)
\( D \) — Diameter of Sphere in Fluid (m)
\( v \) — Velocity of Body or Fluid (m/s)

Explanation: This formula calculates the drag force on a sphere in a viscous fluid, which is proportional to the viscosity, diameter, and velocity.

3. Importance of Drag Force Calculation

Details: Calculating drag force is essential in fluid dynamics for designing systems involving fluid flow around spherical objects, such as in chemical processing, aerospace engineering, and biomedical applications.

4. Using the Calculator

Tips: Enter dynamic viscosity in Pa·s, diameter in meters, and velocity in m/s. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is dynamic viscosity?
A: Dynamic viscosity is a measure of a fluid's resistance to flow when an external force is applied. It quantifies the internal friction within the fluid.

Q2: When is this formula applicable?
A: This formula is valid for Stokes flow conditions, where Reynolds number is very low (Re < 1), typically for slow-moving fluids or small particles.

Q3: What are typical units for these measurements?
A: Dynamic viscosity is measured in Pa·s (Pascal-seconds), diameter in meters, velocity in m/s, and the resulting force in Newtons.

Q4: How does sphere diameter affect drag force?
A: Drag force increases linearly with sphere diameter - doubling the diameter doubles the drag force, assuming other factors remain constant.

Q5: What factors influence dynamic viscosity?
A: Dynamic viscosity depends on temperature, pressure, and the specific properties of the fluid. It typically decreases with increasing temperature for liquids.