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Difficulty: EasyFluid Dynamics and Bernoulli's Principle

Water flows at a steady rate through a horizontal pipe that consists of four distinct sections with different diameters. According to Bernoulli's principle and the continuity equation, arrange the pipe sections in order of their static pressure, from the lowest static pressure to the highest static pressure.

  1. 1Section W: 1-inch diameter
  2. 2Section X: 2-inch diameter
  3. 3Section Y: 3-inch diameter
  4. 4Section Z: 4-inch diameter

Answer

The correct sequence from lowest to highest static pressure is: Section W (1-inch), Section X (2-inch), Section Y (3-inch), Section Z (4-inch).
According to the continuity equation, a fluid travels faster through a narrower section of pipe. According to Bernoulli's principle, an increase in fluid velocity results in a decrease in static pressure. Therefore, the pipe sections with the smallest diameters will have the highest velocities and the lowest static pressures, while the sections with the largest diameters will have the lowest velocities and the highest static pressures.

Step-by-Step Solution

1
Determine the relationship between the pipe's diameter and the fluid's velocity.
The continuity equation indicates that fluid must travel faster through narrower sections to maintain a steady flow rate. Therefore, the smallest diameter has the highest velocity, and the largest diameter has the lowest velocity.
Because the volume of fluid passing through any section per second must remain constant.
2
Determine the relationship between fluid velocity and static pressure.
Bernoulli's principle states that an increase in fluid velocity occurs simultaneously with a decrease in static pressure.
The total energy in a steady, horizontal fluid flow is constant; as kinetic energy (speed) increases, pressure potential energy must decrease.
3
Rank the sections based on these relationships.
Since smallest diameter = highest velocity = lowest pressure, the order from lowest to highest pressure corresponds exactly to the order from smallest to largest diameter.
This allows us to arrange the sections directly by their diameter sizes: 1-inch, 2-inch, 3-inch, and 4-inch.

Key Concept

Fluid Dynamics and Bernoulli's Principle
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Topics

Fluid Dynamics and Bernoulli's Principle

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