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Difficulty: EasyFluid Dynamics and Bernoulli's Principle

A common paint sprayer operates by blowing a stream of fast-moving air across the top of an open vertical tube, with the bottom of the tube submerged in a container of paint. Based on Bernoulli's principle, what is the primary reason the paint rises up the tube?

  1. The fast-moving air creates a region of low static pressure at the top of the tube, allowing atmospheric pressure to push the paint upward.Answer
  2. B
    The high-speed air creates a region of high static pressure at the top of the tube, which pulls the paint upward.
  3. C
    The stream of air compresses the fluid inside the vertical tube, reducing its volume and forcing it upward.
  4. D
    The fast-moving air decreases the weight of the displaced fluid, causing an upward buoyant force.

Answer

The fast-moving air creates a region of low static pressure at the top of the tube, allowing atmospheric pressure to push the paint upward.
According to Bernoulli's principle, an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure. The fast-moving air across the top of the tube creates a localized low-pressure area. The relatively higher atmospheric pressure pushing down on the surface of the paint in the container then forces the liquid up the tube.

Step-by-Step Solution

1
Analyze the relationship between fluid speed and pressure.
The air moving quickly across the top of the tube has a higher velocity than the still air surrounding the container.
This scenario directly sets up an application of Bernoulli's principle.
2
Determine the pressure difference.
Due to its high velocity, the air stream creates an area of low static pressure directly above the open tube.
Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in its static pressure.
3
Evaluate the effect on the fluid in the container.
The standard atmospheric pressure resting on the surface of the paint in the container is greater than the low pressure at the top of the tube, thus forcing the paint upward into the stream.
Fluids naturally move from areas of higher pressure to areas of lower pressure.

Key Concept

Bernoulli's principle establishes an inverse relationship between a fluid's velocity and its static pressure.
Estimated Time:45s
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Topics

Fluid Dynamics and Bernoulli's Principle

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