Consider the system shown below. If a change of 0.7 kPa in the pressure of air causes the brine-mercury interface in the right column to drop by 5 mm in the brine level in the right column while the pressure in the brine pipe remains constant, determine the ratio of A2/A1. Brine pine

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**Hydraulic System Analysis**

Consider the system shown below. If a change of 0.7 kPa in the pressure of air causes the brine–mercury interface in the right column to drop by 5 mm in the brine level in the right column while the pressure in the brine pipe remains constant, determine the ratio of A2/A1.

**Diagram Explanation:**

The given diagram illustrates a hydraulic system consisting of a cylindrical container divided into three layers:
1. **Air Layer:** Occupies the top region of the cylinder.
2. **Water Layer:** Located beneath the air layer.
3. **Mercury Layer:** Situated at the bottom, below the water layer.

To the right of the cylinder, there's a brine pipe filled with brine (a saline solution), with a specific gravity (SG) of 1.1. The brine pipe connects vertically from the top of the cylinder's mercury layer.

The cylinder base has an area denoted as **A1** and the cross-sectional area of the brine pipe is indicated as **A2**.

**Figure Details:**

1. **Pressure Influence:** When the air pressure at the top changes by 0.7 kPa, it affects the mercury and brine levels.
2. **Interface Movement:** The brine–mercury interface in the right column drops by 5 mm as a result.
3. **Constant Pressure in Brine Pipe:** The pressure in the brine pipe remains unchanged despite the air pressure fluctuation.

Given these conditions, the task is to determine the ratio of the area of the pipe (A2) to the area of the cylinder base (A1).

By analyzing the fluid dynamics and applying principles of pressure and specific gravity to the system, you can solve for the desired area ratio.
Transcribed Image Text:**Hydraulic System Analysis** Consider the system shown below. If a change of 0.7 kPa in the pressure of air causes the brine–mercury interface in the right column to drop by 5 mm in the brine level in the right column while the pressure in the brine pipe remains constant, determine the ratio of A2/A1. **Diagram Explanation:** The given diagram illustrates a hydraulic system consisting of a cylindrical container divided into three layers: 1. **Air Layer:** Occupies the top region of the cylinder. 2. **Water Layer:** Located beneath the air layer. 3. **Mercury Layer:** Situated at the bottom, below the water layer. To the right of the cylinder, there's a brine pipe filled with brine (a saline solution), with a specific gravity (SG) of 1.1. The brine pipe connects vertically from the top of the cylinder's mercury layer. The cylinder base has an area denoted as **A1** and the cross-sectional area of the brine pipe is indicated as **A2**. **Figure Details:** 1. **Pressure Influence:** When the air pressure at the top changes by 0.7 kPa, it affects the mercury and brine levels. 2. **Interface Movement:** The brine–mercury interface in the right column drops by 5 mm as a result. 3. **Constant Pressure in Brine Pipe:** The pressure in the brine pipe remains unchanged despite the air pressure fluctuation. Given these conditions, the task is to determine the ratio of the area of the pipe (A2) to the area of the cylinder base (A1). By analyzing the fluid dynamics and applying principles of pressure and specific gravity to the system, you can solve for the desired area ratio.
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