What is the speed of water at point 1 and point 2? Find the pressure at point 1 and point 2.

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What is the speed of water at point 1 and point 2?

Find the pressure at point 1 and point 2.

### Water Flow in Pipes - Calculating Pressure and Volume Transfer

**Problem Statement:**

Water travels through a pipe from point 1 to point 2.

* The pipe descends 5.00 m vertically from point 1 to point 2. 
* At point 1, the cross-sectional area of the pipe is 2.00 m². 
* At point 2, the cross-sectional area of the pipe is 0.500 m².
* The bottom of the pipe (Point 2) is open to the atmosphere, and the top of the pipe (Point 1) is at an unknown pressure.
* You place a bucket below point 2 and find that a volume of water equal to 0.15 m³ falls into the bucket per second.

**Given:**

- Water density: 1000 kg/m³
- Atmospheric pressure: 1.013 x 10⁵ Pa

### Diagram Explanation:

The diagram included in the problem shows a pipe descending from point 1 (located higher) to point 2 (located lower). The pipe curves away as it moves from point 1 to point 2. Point 1 is labeled at the start of the descent, whereas point 2 is labeled at the discharge end of the pipe.

1. **Point 1**: 
    - Cross-sectional area: 2.00 m²
    - Unknown pressure
2. **Point 2**: 
    - Cross-sectional area: 0.500 m²
    - Open to atmosphere, known pressure
    - Discharge rate: 0.15 m³/s

The diagram helps visualize how water flows downward through the pipe and how the cross-sectional area changes from a wider section at the top to a narrower section at the bottom. This change in area and height influences the water's velocity and pressure due to principles outlined in the Bernoulli equation and principles of fluid dynamics.
Transcribed Image Text:### Water Flow in Pipes - Calculating Pressure and Volume Transfer **Problem Statement:** Water travels through a pipe from point 1 to point 2. * The pipe descends 5.00 m vertically from point 1 to point 2. * At point 1, the cross-sectional area of the pipe is 2.00 m². * At point 2, the cross-sectional area of the pipe is 0.500 m². * The bottom of the pipe (Point 2) is open to the atmosphere, and the top of the pipe (Point 1) is at an unknown pressure. * You place a bucket below point 2 and find that a volume of water equal to 0.15 m³ falls into the bucket per second. **Given:** - Water density: 1000 kg/m³ - Atmospheric pressure: 1.013 x 10⁵ Pa ### Diagram Explanation: The diagram included in the problem shows a pipe descending from point 1 (located higher) to point 2 (located lower). The pipe curves away as it moves from point 1 to point 2. Point 1 is labeled at the start of the descent, whereas point 2 is labeled at the discharge end of the pipe. 1. **Point 1**: - Cross-sectional area: 2.00 m² - Unknown pressure 2. **Point 2**: - Cross-sectional area: 0.500 m² - Open to atmosphere, known pressure - Discharge rate: 0.15 m³/s The diagram helps visualize how water flows downward through the pipe and how the cross-sectional area changes from a wider section at the top to a narrower section at the bottom. This change in area and height influences the water's velocity and pressure due to principles outlined in the Bernoulli equation and principles of fluid dynamics.
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