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![### Water Flow and Pressure in a Tank
A large tank of water has a hose connected to it, as depicted in the diagram (Figure 1). The tank is sealed at the top and contains compressed air between the water surface and the top. When the water height \( h \) is 3.50 m, the absolute pressure \( p \) of the compressed air is \( 4.20 \times 10^5 \) Pa. Assume that the air above the water expands at constant temperature, and consider the atmospheric pressure to be \( 1.00 \times 10^5 \) Pa.
**Figure Explanation:**
The diagram shows a cylindrical tank filled with water. The tank has a total height of 4.00 m. The water fills the tank up to height \( h \) and is connected to a hose that extends 1.00 m from the bottom of the tank. The air pressure above the water is depicted as \( p \).
**Problem Part A:**
What is the speed with which water flows out of the hose when \( h = 3.50 \) m?
- **Express your answer in meters per second.**
\[ v = \]
\[ \boxed{\text{Submit}} \]
**Problem Part B:**
As water flows out of the tank, the height \( h \) decreases. Calculate the speed of flow for \( h = 3.10 \) m.
- **Express your answer in meters per second.**
\[ v = \]
\[ \boxed{\text{Submit}} \]
These calculations involve principles of fluid dynamics, specifically Bernoulli's equation and the concept of fluid flow under pressure.](https://content.bartleby.com/qna-images/question/b10c217e-0837-4d3f-89c5-6d9b36b54f81/7097504b-9a18-43f4-9cad-f1e8e9979795/hcruuvc_processed.png)
Transcribed Image Text:### Water Flow and Pressure in a Tank
A large tank of water has a hose connected to it, as depicted in the diagram (Figure 1). The tank is sealed at the top and contains compressed air between the water surface and the top. When the water height \( h \) is 3.50 m, the absolute pressure \( p \) of the compressed air is \( 4.20 \times 10^5 \) Pa. Assume that the air above the water expands at constant temperature, and consider the atmospheric pressure to be \( 1.00 \times 10^5 \) Pa.
**Figure Explanation:**
The diagram shows a cylindrical tank filled with water. The tank has a total height of 4.00 m. The water fills the tank up to height \( h \) and is connected to a hose that extends 1.00 m from the bottom of the tank. The air pressure above the water is depicted as \( p \).
**Problem Part A:**
What is the speed with which water flows out of the hose when \( h = 3.50 \) m?
- **Express your answer in meters per second.**
\[ v = \]
\[ \boxed{\text{Submit}} \]
**Problem Part B:**
As water flows out of the tank, the height \( h \) decreases. Calculate the speed of flow for \( h = 3.10 \) m.
- **Express your answer in meters per second.**
\[ v = \]
\[ \boxed{\text{Submit}} \]
These calculations involve principles of fluid dynamics, specifically Bernoulli's equation and the concept of fluid flow under pressure.
![**Part C**
Calculate the speed of flow for \( h = 2.10 \, \text{m} \).
**Express your answer in meters per second.**
\( v = \) [input box] m/s
- [Submit Button]
- [Request Answer Button]
---
**Part D**
At what value of \( h \) does the flow stop?
**Express your answer in meters.**
\( h = \) [input box] m
- [Submit Button]
- [Request Answer Button]](https://content.bartleby.com/qna-images/question/b10c217e-0837-4d3f-89c5-6d9b36b54f81/7097504b-9a18-43f4-9cad-f1e8e9979795/ktme3zj_processed.png)
Transcribed Image Text:**Part C**
Calculate the speed of flow for \( h = 2.10 \, \text{m} \).
**Express your answer in meters per second.**
\( v = \) [input box] m/s
- [Submit Button]
- [Request Answer Button]
---
**Part D**
At what value of \( h \) does the flow stop?
**Express your answer in meters.**
\( h = \) [input box] m
- [Submit Button]
- [Request Answer Button]
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