Continuity Equation (Fluid)

📊 beginner

$$A_1 v_1 = A_2 v_2$$

Mass conservation for incompressible flow: product of cross-sectional area and speed is constant.

Variables & Units

$A_1, A_2$

Cross-sectional areas

Unit: $\text{m}^2$

$v_1, v_2$

Flow speeds

Unit: $\text{m/s}$

Key Information

📐 Derived From

Mass conservation: $\rho A v = \text{constant}$

💡 Example

Pipe narrows from $A_1=0.01\,\text{m}^2$ to $A_2=0.002\,\text{m}^2$, $v_1=3\,\text{m/s}$: $v_2 = (0.01 \times 3)/0.002 = 15\,\text{m/s}$.

🔧 Applications

Hydraulic systems, cardiovascular flow, nozzle design

⚠️ Constraints

Incompressible fluid, steady flow

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