Velocity Of Air At Duct Section 1 Using Continuity Equation Calculator

Continuity Equation:

\[ V_1 = \frac{A_2 \times V_2}{A_1} \]

Cross-Sectional Area of Duct at Section 2 (A₂):

m²

Velocity of Air at Section 2 (V₂):

m/s

Cross-Sectional Area of Duct at Section 1 (A₁):

m²

Velocity of Air at Section 1 (V₁):

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1. What is the Continuity Equation?

The Continuity Equation is a fundamental principle in fluid dynamics that states that for an incompressible fluid flowing through a pipe, the mass flow rate must remain constant. This means that the product of cross-sectional area and velocity at any two points in the flow must be equal.

2. How Does the Calculator Work?

The calculator uses the Continuity Equation:

\[ V_1 = \frac{A_2 \times V_2}{A_1} \]

Where:

\( V_1 \) — Velocity of Air at Section 1 (m/s)
\( A_2 \) — Cross-Sectional Area of Duct at Section 2 (m²)
\( V_2 \) — Velocity of Air at Section 2 (m/s)
\( A_1 \) — Cross-Sectional Area of Duct at Section 1 (m²)

Explanation: The equation demonstrates that when a fluid flows through a duct of varying cross-section, the velocity increases where the cross-section decreases, and vice versa, while maintaining constant mass flow rate.

3. Importance of Continuity Equation

Details: The Continuity Equation is essential for designing and analyzing fluid flow systems, including HVAC systems, piping networks, and aerodynamic applications. It helps engineers predict flow behavior and optimize system performance.

4. Using the Calculator

Tips: Enter all three values in appropriate units (cross-sectional areas in m², velocities in m/s). All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What assumptions does the Continuity Equation make?
A: The equation assumes incompressible flow, steady flow conditions, and no mass accumulation within the control volume.

Q2: Can this equation be used for compressible fluids?
A: For compressible fluids, the equation must be modified to account for density changes using the mass continuity equation: ρ₁A₁V₁ = ρ₂A₂V₂.

Q3: What are typical applications of this equation?
A: HVAC system design, pipe flow analysis, wind tunnel testing, and any application involving fluid flow through conduits of varying cross-section.

Q4: How accurate is this calculation for real-world applications?
A: The equation provides theoretical values. Real-world applications may require additional factors such as friction losses, turbulence, and fluid properties.

Q5: What units should I use for the inputs?
A: Use consistent SI units: square meters (m²) for areas and meters per second (m/s) for velocities for accurate results.