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The image shows a problem related to fluid mechanics involving a manometer and a system of connected fluids. Here's a summary of the key points:

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**Question 1 (5 points)**

A container with multiple fluids is connected to a mercury manometer, as shown in Figure 1. The tasks are:

a. Find the specific gravities and heights of the fluid columns.
b. Determine the manometric pressure at point A.
c. Finally, determine the height of a mercury column that exerts the same pressure as at point A.

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**Figure 1** shows a manometer with three sections of fluids:
- **Gas (ρ_gas = 850 kg/m³)** on top of the system, height of 0.4 meters.
- **Water (ρ_water = 1000 kg/m³)**, height of 0.2 meters.
- **Mercury (ρ_Hg = 13,600 kg/m³)**, height unknown but this part likely connects to the pressure exerted.

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### Solution Plan:

#### a. Specific gravities and heights:
- **Specific gravity** is calculated as the ratio of the density of a fluid to the density of water. 
    - For the gas: \( S_g = \frac{\rho_{gas}}{\rho_{water}} \).
    - For mercury: \( S_{Hg} = \frac{\rho_{Hg}}{\rho_{water}} \).

#### b. Manometric pressure at point A:
   The pressure at point A can be found using the hydrostatic pressure formula:
   
   \[
   P_A = P_0 + \rho_{fluid}gh
   \]
   
   Where \( P_0 \) is the atmospheric pressure, \( \rho_{fluid} \) is the density, \( g \) is gravitational acceleration (9.81 m/s²), and \( h \) is the height of each fluid.

#### c. Equivalent height of mercury column:
   The height of a mercury column that exerts the same pressure as point A can be calculated by setting the pressure from part b equal to the pressure exerted by the mercury column and solving for height.

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I can now perform the calculations based on these details.

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A container with multiple fluids is connected to a mercury manometer, as shown in Figure 1. The tasks are: a. Find the specific gravities and heights of the fluid columns. b. Determine the manometric pressure at point A. c. Finally, determine the height of a mercury column that exerts the same pressure as at point A.

Solve a fluid mechanics problem involving manometric pressure and specific gravity of fluids. This question covers key concepts in hydrostatics and manometry, and includes a detailed step-by-step solution suitable for undergraduate students.

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