Concept:In the Continuity Equation, the mass flow rate must balance: \( \rho_1 A_1 v_1 = \rho_2 A_2 v_2 \).
Formula:$$ \rho_2 = \rho_1 \left( \frac{A_1 v_1}{A_2 v_2} \right) $$
Solution:- In this analogy, Area (\( A \)) decreases because three lanes turn into one.
- Simultaneously, the speed (\( v \)) of the cars also decreases.
- For the product \( \rho A v \) to balance out, the density (\( \rho \)) must increase dramatically. Cars pack closely together.
- Since the "density" of the fluid changes sharply, the traffic acts as a highly compressible fluid.
Why other options are incorrect:If it were an incompressible fluid, density would be constant, and decreasing the area would force the speed \( v \) to increase, not decrease. Real traffic does not act incompressible.
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