Relative Velocity Of Fluid With Respect To Body Given Drag Force Calculator

Formula Used:

\[ V_r = \sqrt{\frac{F_{dD} \times 2}{A_p \times \rho_{mf} \times C_d}} \]

Drag Force by Fluid on Body (F_dD):

Projected Area of Body (A_p):

m²

Density of Moving Fluid (ρ_mf):

kg/m³

Drag Coefficient for Fluid Flow (C_d):

Relative Velocity of Fluid Past Body (V_r):

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1. What is Relative Velocity of Fluid Past Body?

Relative Velocity of Fluid Past Body is the velocity of the fluid flowing parallel to a body imparting force on its surface. It represents the speed difference between the fluid and the object moving through it.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_r = \sqrt{\frac{F_{dD} \times 2}{A_p \times \rho_{mf} \times C_d}} \]

Where:

\( V_r \) — Relative velocity of fluid past body (m/s)
\( F_{dD} \) — Drag force by fluid on body (N)
\( A_p \) — Projected area of body (m²)
\( \rho_{mf} \) — Density of moving fluid (kg/m³)
\( C_d \) — Drag coefficient for fluid flow (dimensionless)

Explanation: This formula calculates the relative velocity between a fluid and a body based on the drag force experienced by the body, its projected area, fluid density, and drag coefficient.

3. Importance of Relative Velocity Calculation

Details: Calculating relative velocity is crucial for understanding fluid-structure interactions, designing aerodynamic and hydrodynamic systems, and predicting drag forces in various engineering applications.

4. Using the Calculator

Tips: Enter drag force in newtons, projected area in square meters, fluid density in kg/m³, and drag coefficient (dimensionless). All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is drag coefficient?
A: Drag coefficient is a dimensionless quantity that quantifies the drag or resistance of an object in a fluid environment. It depends on the object's shape and surface properties.

Q2: How is projected area defined?
A: Projected area is the two-dimensional area of a three-dimensional object obtained by projecting its shape onto a plane perpendicular to the flow direction.

Q3: What factors affect relative velocity?
A: Relative velocity is influenced by drag force, object geometry, fluid properties (density, viscosity), and the object's orientation relative to the flow.

Q4: When is this formula applicable?
A: This formula is applicable for calculating relative velocity when drag force, projected area, fluid density, and drag coefficient are known for an object in a fluid flow.

Q5: What are typical drag coefficient values?
A: Drag coefficients vary widely: sphere (~0.47), streamlined body (~0.04-0.1), flat plate perpendicular to flow (~1.28), and automobile (~0.25-0.35).