The figure shows a pipe reducing section for which D₁ = 8 cm and D₂ = 5 cm. Water is flowing in the pipe. If V₁ = 5 m/s and the manometer reads h = = 0.58 m, what is the force acting on the flange bolts? The liquid in the manometer is mercury. h 2

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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The figure illustrates a pipe reducing section where the diameter of the wider section (D₁) is 8 cm and the diameter of the narrower section (D₂) is 5 cm. Water is flowing through the pipe. The flow velocity at section 1 (V₁) is 5 m/s, and the manometer indicates a height (h) of 0.58 m. The task is to calculate the force acting on the flange bolts. The manometer fluid is mercury.

### Diagram Explanation

- **Pipe Section:** The diagram shows a pipe with a reducing section, meaning it transitions from a larger diameter to a smaller one.
- **Flange Bolts:** Two areas are highlighted, labeled as ➀ and ➁, where the flange bolts are located. These hold the pipe sections together.
- **Manometer:** A U-shaped device is connected at the reduction section, filled with mercury, which measures the pressure difference between the two sections of the pipe.
- **Measurement:** The height difference (h) in the mercury within the manometer is 0.58 meters, indicating the pressure drop due to the reduction in diameter.

This setup is commonly used to demonstrate principles of fluid dynamics, such as Bernoulli's principle and the continuity equation, by analyzing changes in pressure and velocity when the diameter of a pipe changes.
Transcribed Image Text:The figure illustrates a pipe reducing section where the diameter of the wider section (D₁) is 8 cm and the diameter of the narrower section (D₂) is 5 cm. Water is flowing through the pipe. The flow velocity at section 1 (V₁) is 5 m/s, and the manometer indicates a height (h) of 0.58 m. The task is to calculate the force acting on the flange bolts. The manometer fluid is mercury. ### Diagram Explanation - **Pipe Section:** The diagram shows a pipe with a reducing section, meaning it transitions from a larger diameter to a smaller one. - **Flange Bolts:** Two areas are highlighted, labeled as ➀ and ➁, where the flange bolts are located. These hold the pipe sections together. - **Manometer:** A U-shaped device is connected at the reduction section, filled with mercury, which measures the pressure difference between the two sections of the pipe. - **Measurement:** The height difference (h) in the mercury within the manometer is 0.58 meters, indicating the pressure drop due to the reduction in diameter. This setup is commonly used to demonstrate principles of fluid dynamics, such as Bernoulli's principle and the continuity equation, by analyzing changes in pressure and velocity when the diameter of a pipe changes.
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