Velocity Of Air At Duct Section 2 Using Continuity Equation Calculator

Continuity Equation:

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

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

m²

Velocity of Air at Section 1 (V₁):

m/s

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

m²

Velocity of Air at Section 2 (V₂):

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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:

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

Where:

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

Explanation: The equation demonstrates that when a fluid flows through a constricted section (smaller area), its velocity increases, and when it flows through an expanded section (larger area), its velocity decreases.

3. Importance of Continuity Equation

Details: The Continuity Equation is crucial 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 cross-sectional areas in square meters (m²) and velocities in meters per second (m/s). All values must be positive numbers, and cross-sectional areas must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What assumptions does the Continuity Equation make?
A: The equation assumes that the fluid is incompressible, the flow is steady, and there are no fluid sources or sinks between the two sections.

Q2: Can this equation be used for compressible fluids?
A: For compressible fluids, the mass flow rate remains constant, but the equation needs to account for density changes: \( \rho_1 A_1 V_1 = \rho_2 A_2 V_2 \).

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 varying cross-sections.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for ideal conditions. Real-world factors like friction, turbulence, and viscosity may cause deviations from theoretical values.

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. The calculator will provide results in m/s.