As air flows downward through the venturi constriction, it...

As air flows downward through the venturi constriction, it creates a low pressure at $A$ that causes ethyl alcohol to rise in the tube and be drawn into the air stream. Determine the velocity of the air as it passes through the tube at $B$ in order to do this. The air is discharged to the atmosphere at $C .$ Take $\rho_{e a}=789 \mathrm{~kg} / \mathrm{m}^{3}$ and $\rho_{a}=1.225 \mathrm{~kg} / \mathrm{m}^{3}$.

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Key Concepts

Venturi Effect

This concept explains that as fluid flows through a constricted section of a pipe, its velocity increases while its static pressure decreases. It is fundamental in understanding why a low pressure region is created at the constriction, which is essential for the operation of devices that rely on pressure differences.

Bernoulli's Principle

Bernoulli's equation is used to relate the pressure, velocity, and elevation of a fluid along a streamline. It demonstrates that an increase in the speed of the fluid occurs simultaneously with a decrease in its pressure or potential energy, providing the theoretical basis for analyzing fluid flow in systems with varying cross-sectional areas.

Continuity Equation

This principle of mass conservation in fluid dynamics states that for an incompressible fluid, the product of the flow area and velocity is constant along the stream tube. It is crucial for linking the fluid velocities in sections of differing areas, ensuring that the mass flow rate remains constant across the system.

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