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Zorluk: OrtaFluid Dynamics and Bernoulli's Principle

During routine maintenance of a municipal water line, engineers observe that a thick layer of mineral scale has formed inside a section of a horizontal supply pipe. This scale acts as a partial blockage, significantly reducing the pipe's interior cross-sectional area in that specific location. Assuming the flow rate of water through the system remains steady, how are the water's velocity and static pressure affected as it passes through this narrowed section?

  1. A
    The water's velocity increases, and its static pressure also increases due to the confined space.
  2. B
    The water's velocity decreases due to the restricted opening, causing the static pressure to drop.
  3. The water's velocity increases, and its static pressure decreases.Cevap
  4. D
    The water's velocity remains constant, but its static pressure increases because the liquid is compressed.

Cevap

The water's velocity increases, and its static pressure decreases.
In a closed, continuous fluid system, an incompressible liquid like water must maintain a constant flow rate. When it encounters a constriction (like the mineral scale buildup), the only way the same volume of water can get through the smaller opening in the same amount of time is to speed up (principle of continuity). As the velocity increases, Bernoulli's principle dictates that the static pressure must decrease so that the total energy of the fluid flow remains constant.

Adım Adım Çözüm

1
Determine the change in velocity through the narrowed pipe section.
The velocity of the water increases.
Because water is an incompressible fluid, the same volume of water must pass through the restricted area in the same amount of time. This relies on the principle of continuity (A1V1=A2V2A_1V_1 = A_2V_2). To maintain the flow rate through a smaller cross-sectional area (AA), the velocity (VV) must increase.
2
Determine the change in static pressure based on the new velocity.
The static pressure of the water decreases.
According to Bernoulli's principle, the total mechanical energy in a steady horizontal fluid flow remains constant. When the water's kinetic energy increases (due to higher velocity), its potential energy—manifested as static pressure against the pipe walls—must decrease proportionally to conserve energy.

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Fluid Dynamics and Bernoulli's Principle
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Fluid Dynamics and Bernoulli's Principle

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