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A fluid manometer is open to the atmosphere as shown in figurel. If the gage pressure of the pressurized air is 0.05MPa, find the differential height h3 if hl= 50cm and h2= 35cm.

A fluid manometer is open to the atmosphere as shown in figurel. If the gage pressure of the pressurized air is 0.05MPa, find the differential height h3 if hl= 50cm and h2= 35cm.

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**Figure 1: Differential Manometer with Multiple Fluids** **Diagram Explanation:** This diagram illustrates a differential manometer used to measure the pressure difference between two points in a fluid system that involves multiple fluids with different specific gravities (SG). - **Methane Chamber (Left Side)**: - Contains methane gas with a specific gravity (SG) of 0.47. - There is a marked interface where the air is present. - **Fluid Columns and Heights**: - The manometer contains mercury (SG = 13.6) in the middle section, as denoted by the shaded area with upward and downward arrows. - The manometer shows three different heights: - **h1**: The height of the mercury column on the left side. - **h2**: The height of the mercury column on the right side, it represents the height difference. - **h3**: The height of a fluid column on the right side, designated by the presence of gasoline. - **Gasoline Column (Right Side)**: - The right side of the manometer contains gasoline with a specific gravity (SG) of 0.70. - There is a marker at point 2 which might represent a pressure measurement. **Key Points**: - The manometer uses mercury, methane, and gasoline, all of which have different specific gravities affecting the pressure readings. - Measurements involving multiple fluids and corresponding heights (h1, h2, h3) help in calculating pressure differences. Understanding and analyzing this type of manometer setup requires balancing the pressure exerted by the different fluids in their respective columns. This balance helps determine the pressure difference between point 1 (in the methane gas region) and point 2 (in the gasoline region).
Transcribed Image Text:**Figure 1: Differential Manometer with Multiple Fluids** **Diagram Explanation:** This diagram illustrates a differential manometer used to measure the pressure difference between two points in a fluid system that involves multiple fluids with different specific gravities (SG). - **Methane Chamber (Left Side)**: - Contains methane gas with a specific gravity (SG) of 0.47. - There is a marked interface where the air is present. - **Fluid Columns and Heights**: - The manometer contains mercury (SG = 13.6) in the middle section, as denoted by the shaded area with upward and downward arrows. - The manometer shows three different heights: - **h1**: The height of the mercury column on the left side. - **h2**: The height of the mercury column on the right side, it represents the height difference. - **h3**: The height of a fluid column on the right side, designated by the presence of gasoline. - **Gasoline Column (Right Side)**: - The right side of the manometer contains gasoline with a specific gravity (SG) of 0.70. - There is a marker at point 2 which might represent a pressure measurement. **Key Points**: - The manometer uses mercury, methane, and gasoline, all of which have different specific gravities affecting the pressure readings. - Measurements involving multiple fluids and corresponding heights (h1, h2, h3) help in calculating pressure differences. Understanding and analyzing this type of manometer setup requires balancing the pressure exerted by the different fluids in their respective columns. This balance helps determine the pressure difference between point 1 (in the methane gas region) and point 2 (in the gasoline region).
### Problem Statement **1. A fluid manometer is open to the atmosphere as shown in figure 1. If the gage pressure of the pressurized air is 0.05 MPa, find the differential height h3 if h1 = 50 cm and h2 = 35 cm.** In this problem, we are given a fluid manometer which is open to the atmosphere. The given parameters include: - Gage pressure of the pressurized air: 0.05 MPa - Height \( h1 \): 50 cm - Height \( h2 \): 35 cm We are required to find the differential height \( h3 \). ### Explanation of Diagram (Figure 1) While the text mentions a figure (Figure 1), it is not provided in the image above. Normally, in such problems, a manometer would be depicted as a U-shaped tube with one side open to the atmosphere and the other connected to a pressurized container. ### Steps to Solve the Problem 1. **Understand the pressure readings:** - Gage pressure is the pressure relative to atmospheric pressure. - In a manometer, the difference in the column heights of the manometer fluid can be used to determine the pressure difference. 2. **Calculate the differential height \( h3 \):** - The differential height \( h3 \) can be found using the heights of the fluid columns on the manometer. The typical formula used in such calculations is: \[ \text{Pressure Difference} = \rho \cdot g \cdot h \] where \(\rho\) is the density of the fluid, \(g\) is the acceleration due to gravity (9.8 m/s²), and \(h\) is the height difference between the two columns. In this case: \[ h3 = h1 - h2 = 50 \, \text{cm} - 35 \, \text{cm} \] ### Solution \[ h3 = 15 \, \text{cm} \] Therefore, the differential height \( h3 \) is 15 cm. ### Important Notes - Always ensure to convert units to the SI system if required. - Clearly understand the relationship between the given pressures and the heights of the fluid columns in a manometric setup. For a comprehensive understanding, refer to the diagram
Transcribed Image Text:### Problem Statement **1. A fluid manometer is open to the atmosphere as shown in figure 1. If the gage pressure of the pressurized air is 0.05 MPa, find the differential height h3 if h1 = 50 cm and h2 = 35 cm.** In this problem, we are given a fluid manometer which is open to the atmosphere. The given parameters include: - Gage pressure of the pressurized air: 0.05 MPa - Height \( h1 \): 50 cm - Height \( h2 \): 35 cm We are required to find the differential height \( h3 \). ### Explanation of Diagram (Figure 1) While the text mentions a figure (Figure 1), it is not provided in the image above. Normally, in such problems, a manometer would be depicted as a U-shaped tube with one side open to the atmosphere and the other connected to a pressurized container. ### Steps to Solve the Problem 1. **Understand the pressure readings:** - Gage pressure is the pressure relative to atmospheric pressure. - In a manometer, the difference in the column heights of the manometer fluid can be used to determine the pressure difference. 2. **Calculate the differential height \( h3 \):** - The differential height \( h3 \) can be found using the heights of the fluid columns on the manometer. The typical formula used in such calculations is: \[ \text{Pressure Difference} = \rho \cdot g \cdot h \] where \(\rho\) is the density of the fluid, \(g\) is the acceleration due to gravity (9.8 m/s²), and \(h\) is the height difference between the two columns. In this case: \[ h3 = h1 - h2 = 50 \, \text{cm} - 35 \, \text{cm} \] ### Solution \[ h3 = 15 \, \text{cm} \] Therefore, the differential height \( h3 \) is 15 cm. ### Important Notes - Always ensure to convert units to the SI system if required. - Clearly understand the relationship between the given pressures and the heights of the fluid columns in a manometric setup. For a comprehensive understanding, refer to the diagram
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