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Difficulty: MediumFluid Dynamics and Bernoulli's Principle

A mechanical eductor (or jet pump) uses a primary fluid flowing through a converging nozzle to extract a secondary fluid from a lower tank. As the primary fluid accelerates through the narrowest section of the nozzle, how does its static pressure change, and what is the resulting effect on the secondary fluid?

  1. A
    The static pressure rises proportionally with the fluid's velocity, creating a force that pushes the secondary fluid forward.
  2. B
    The increased friction against the narrow nozzle walls creates a high-pressure zone that drives the secondary fluid upward.
  3. The static pressure drops below the surrounding pressure, creating a suction effect that draws the secondary fluid into the main stream.Answer
  4. D
    The static pressure remains constant because liquids are incompressible, and the fluids mix solely due to physical contact.

Answer

The static pressure drops below the surrounding pressure, creating a suction effect that draws the secondary fluid into the main stream.
The correct answer accurately applies Bernoulli's principle, which states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure. In an eductor, the narrow nozzle accelerates the primary fluid, causing a significant pressure drop. This localized low-pressure zone acts as a vacuum, drawing the secondary fluid from the tank into the main flow.

Step-by-Step Solution

1
Analyze the fluid flow through the converging nozzle.
The cross-sectional area of the nozzle decreases, which forces the fluid velocity to increase in order to maintain a constant flow rate (continuity principle).
Understanding how area affects velocity is the first step in applying fluid dynamics.
2
Apply Bernoulli's principle to the high-velocity region.
According to Bernoulli's equation, an increase in fluid velocity (kinetic energy) must be accompanied by a decrease in static pressure to conserve total mechanical energy.
This establishes the inverse relationship between velocity and static pressure.
3
Determine the physical consequence of the lowered static pressure.
The decreased static pressure in the narrow section becomes lower than the atmospheric pressure acting on the secondary fluid, creating a pressure differential (suction) that draws the secondary fluid up into the eductor.
This links the theoretical physics concept directly to the mechanical action described in the problem.

Key Concept

As a fluid's velocity increases, its static pressure decreases, which can be utilized to create suction in mechanical systems.
Estimated Time:1m 0s
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Topics

Fluid Dynamics and Bernoulli's Principle

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