Cross-Sectional Area Of Duct At Section 1 Using Continuity Equation Calculator

Continuity Equation:

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

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

m²

Velocity of Air at Section 2 (V₂):

m/s

Velocity of Air at Section 1 (V₁):

m/s

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

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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 or duct, the mass flow rate must remain constant. This means that the product of cross-sectional area and velocity at any two points in the system must be equal.

2. How Does the Calculator Work?

The calculator uses the continuity equation:

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

Where:

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

Explanation: The equation is derived from the principle of conservation of mass, assuming steady, incompressible flow through a closed system.

3. Importance of Continuity Equation

Details: The continuity equation is essential for designing and analyzing fluid flow systems, including HVAC ducts, piping networks, and ventilation systems. It helps engineers determine appropriate duct sizes and predict flow behavior.

4. Using the Calculator

Tips: Enter all values in appropriate units (m² for areas, m/s for velocities). All input values must be positive numbers. The calculator will compute the cross-sectional area at section 1 based on the continuity principle.

5. Frequently Asked Questions (FAQ)

Q1: What assumptions are made in the continuity equation?
A: The equation assumes steady, incompressible flow through a closed system with no mass accumulation or loss.

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 network analysis, ventilation design, and any system involving fluid flow through conduits.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for ideal conditions, but real-world factors like friction losses and turbulence may affect actual results.

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.