The diagram illustrates a cylindrical tank filled with water and covered by air at the top. A manometer is attached to measure the pressure of the air above the water. Here are the key elements:1. **Water Tank**: - The tank contains water up to a height of $ H $. - Above the water, there is a column of air with a height $ h $.2. **Manometer**: - A pressure gauge is present at the top to measure the air pressure inside the tank.3. **Attached Tube**: - The tube is bent and open to the atmosphere at the left side. - The tube is filled with a liquid (possibly mercury or any heavier liquid than water) up to a height $ L $. - The height from the bottom of the tube to the liquid surface is $ \ell $.This setup is typically used to study fluid dynamics and the behavior of liquids under pressure in closed systems. The combination of the water level and air pressure above it, along with the liquid in the tube, can be used to analyze principles like Pascal’s Law and the concept of hydrostatic pressure. A pressurized tank of water is used to create a fountain, as illustrated. Assume that the water's free surface area in the tank is very large relative to the pipe's cross-sectional area, which is circular with diameter $ d = 1.0 \, \text{cm} $. The small pipe bend has height $ \ell = 10.0 \, \text{cm} $. At the instant when $ h = 0.75 \, \text{m} $, $ H = 2.5 \, \text{m} $, and the gauge measures a pressure of $ p_{\text{gauge}} = 20.0 \, \text{kPa} $, the water spray reaches a height $ L $ above the pipe exit.Neglecting viscous effects, determine the height of the spray, $ L $.

Answered: L んー h air

Engineering

Mechanical Engineering

L んー h air

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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The diagram illustrates a cylindrical tank filled with water and covered by air at the top. A manometer is attached to measure the pressure of the air above the water. Here are the key elements:

1. **Water Tank**:
- The tank contains water up to a height of $ H $.
- Above the water, there is a column of air with a height $ h $.

2. **Manometer**:
- A pressure gauge is present at the top to measure the air pressure inside the tank.

3. **Attached Tube**:
- The tube is bent and open to the atmosphere at the left side.
- The tube is filled with a liquid (possibly mercury or any heavier liquid than water) up to a height $ L $.
- The height from the bottom of the tube to the liquid surface is $ \ell $.

This setup is typically used to study fluid dynamics and the behavior of liquids under pressure in closed systems. The combination of the water level and air pressure above it, along with the liquid in the tube, can be used to analyze principles like Pascal’s Law and the concept of hydrostatic pressure.

A pressurized tank of water is used to create a fountain, as illustrated. Assume that the water's free surface area in the tank is very large relative to the pipe's cross-sectional area, which is circular with diameter $ d = 1.0 \, \text{cm} $. The small pipe bend has height $ \ell = 10.0 \, \text{cm} $. At the instant when $ h = 0.75 \, \text{m} $, $ H = 2.5 \, \text{m} $, and the gauge measures a pressure of $ p_{\text{gauge}} = 20.0 \, \text{kPa} $, the water spray reaches a height $ L $ above the pipe exit.

Neglecting viscous effects, determine the height of the spray, $ L $.

Expert Solution

Step 1

$Given d = 1 cm l = 10 cm h = 0.75 m H = 2.5 m P_{guage} = 20.0 kPa$

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