Cross-Sectional Area Of Duct At Section 2 Using Continuity Equation Calculator

Continuity Equation:

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

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

m²

Velocity of Air at Section 1 (V₁):

m/s

Velocity of Air at Section 2 (V₂):

m/s

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

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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 product of the cross-sectional area and the fluid velocity remains constant. This equation is derived from the principle of conservation of mass.

2. How Does the Calculator Work?

The calculator uses the Continuity Equation:

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

Where:

\( A_1 \) — Cross-sectional area at section 1 (m²)
\( V_1 \) — Velocity of air at section 1 (m/s)
\( V_2 \) — Velocity of air at section 2 (m/s)
\( A_2 \) — Cross-sectional area at section 2 (m²)

Explanation: The equation shows that as the cross-sectional area decreases, the velocity increases, and vice versa, to maintain constant mass flow rate.

3. Importance of Continuity Equation

Details: The Continuity Equation is crucial for designing duct systems, ventilation systems, and any fluid transport system where maintaining proper flow characteristics is essential. It helps engineers determine appropriate duct sizes and predict flow behavior.

4. Using the Calculator

Tips: Enter cross-sectional area at section 1 in square meters, velocity at section 1 in meters per second, and velocity at section 2 in meters per second. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions behind the Continuity Equation?
A: The equation assumes 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 equation needs to be modified to account for density changes: \( \rho_1 A_1 V_1 = \rho_2 A_2 V_2 \), where ρ is density.

Q3: What are typical applications of this equation?
A: HVAC system design, pipe flow calculations, ventilation systems, and any application involving fluid transport through conduits.

Q4: How accurate is this calculation for real-world applications?
A: For ideal conditions with smooth, constant-diameter ducts and steady flow, it's very accurate. Real-world factors like friction, turbulence, and fittings may require additional considerations.

Q5: What units should I use for the inputs?
A: The calculator uses SI units: square meters for area and meters per second for velocity. Make sure all inputs are in consistent units for accurate results.