Consider a U-tube manometer used to measure the density pa of liquid A, as shown below. Mercury is used as the base liquid for the manometer with density Phg = 13600kg/m³. If hng = 5mm and ha = 22.4 mm, find Pa. V ha Pa Phg A hng

Elements Of Electromagnetics
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**U-Tube Manometer for Density Measurement**

**Description:**

Consider a U-tube manometer used to measure the density \( \rho_a \) of liquid A, as shown in the diagram. Mercury is used as the base liquid for the manometer with density \( \rho_{hg} = 13600 \, \text{kg/m}^3 \).

The diagram shows a U-tube partially filled with two liquids:

- The left arm contains liquid A with density \( \rho_a \) and height \( h_a = 22.4 \, \text{mm} \).
- The right arm contains mercury with density \( \rho_{hg} \) and height \( h_{hg} = 5 \, \text{mm} \).

The liquid levels in the U-tube are aligned to a reference line indicating the equilibrium state.

**Objective:**

To find the density \( \rho_a \) of liquid A using the given measurements.

**Diagram Explanation:**

- The diagram consists of a U-shaped tube with two arms.
- The left side (red) represents liquid A with its respective height \( h_a \).
- The right side (blue) represents mercury with its respective height \( h_{hg} \).
- Reference lines and symbols indicate the relative heights of the liquids in each arm.

The pressure balance at equilibrium and these measurements can be used to calculate the unknown density \( \rho_a \).
Transcribed Image Text:**U-Tube Manometer for Density Measurement** **Description:** Consider a U-tube manometer used to measure the density \( \rho_a \) of liquid A, as shown in the diagram. Mercury is used as the base liquid for the manometer with density \( \rho_{hg} = 13600 \, \text{kg/m}^3 \). The diagram shows a U-tube partially filled with two liquids: - The left arm contains liquid A with density \( \rho_a \) and height \( h_a = 22.4 \, \text{mm} \). - The right arm contains mercury with density \( \rho_{hg} \) and height \( h_{hg} = 5 \, \text{mm} \). The liquid levels in the U-tube are aligned to a reference line indicating the equilibrium state. **Objective:** To find the density \( \rho_a \) of liquid A using the given measurements. **Diagram Explanation:** - The diagram consists of a U-shaped tube with two arms. - The left side (red) represents liquid A with its respective height \( h_a \). - The right side (blue) represents mercury with its respective height \( h_{hg} \). - Reference lines and symbols indicate the relative heights of the liquids in each arm. The pressure balance at equilibrium and these measurements can be used to calculate the unknown density \( \rho_a \).
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