2.74 A tank of cross-sectional area A is filled with a liquid of specific weight y₁ as shown in Fig. P2.74a. Show that when a cylinder of specific weight 72 and volume Vis floated in the liquid (see Fig. P2.74b), the liquid level rises by an amount Ah = (y2/Y₁)V/A. ▼ V1 Ah (a) FIGURE P2.74 V Y2 (b)
2.74 A tank of cross-sectional area A is filled with a liquid of specific weight y₁ as shown in Fig. P2.74a. Show that when a cylinder of specific weight 72 and volume Vis floated in the liquid (see Fig. P2.74b), the liquid level rises by an amount Ah = (y2/Y₁)V/A. ▼ V1 Ah (a) FIGURE P2.74 V Y2 (b)
Chapter2: Loads On Structures
Section: Chapter Questions
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Explain (Fluids
![**Problem 2.74:**
A tank of cross-sectional area \( A \) is filled with a liquid of specific weight \( \gamma_1 \) as shown in Fig. P2.74a. Show that when a cylinder of specific weight \( \gamma_2 \) and volume \( \mathcal{V} \) is floated in the liquid (see Fig. P2.74b), the liquid level rises by an amount:
\[
\Delta h = (\gamma_2 / \gamma_1) \mathcal{V} / A.
\]
**Figures Explanation:**
- **Figure P2.74a**: This figure shows a tank filled with a liquid at an initial level. The liquid has a specific weight \( \gamma_1 \).
- **Figure P2.74b**: This figure shows the same tank with a cylinder submerged in the liquid. The cylinder has a specific weight \( \gamma_2 \) and volume \( \mathcal{V} \). The liquid level rises by \( \Delta h \) due to the submerged cylinder.
The illustration includes:
- The cross-sectional area of the tank \( A \).
- The original liquid level before the cylinder is added.
- The increased liquid level indicated by \( \Delta h \) after the cylinder is placed in the tank.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b3f294e-d3c8-4475-8e8e-f2b525027412%2F9acd10e4-e5aa-48a7-85d8-230e25d08368%2Fov73qjb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 2.74:**
A tank of cross-sectional area \( A \) is filled with a liquid of specific weight \( \gamma_1 \) as shown in Fig. P2.74a. Show that when a cylinder of specific weight \( \gamma_2 \) and volume \( \mathcal{V} \) is floated in the liquid (see Fig. P2.74b), the liquid level rises by an amount:
\[
\Delta h = (\gamma_2 / \gamma_1) \mathcal{V} / A.
\]
**Figures Explanation:**
- **Figure P2.74a**: This figure shows a tank filled with a liquid at an initial level. The liquid has a specific weight \( \gamma_1 \).
- **Figure P2.74b**: This figure shows the same tank with a cylinder submerged in the liquid. The cylinder has a specific weight \( \gamma_2 \) and volume \( \mathcal{V} \). The liquid level rises by \( \Delta h \) due to the submerged cylinder.
The illustration includes:
- The cross-sectional area of the tank \( A \).
- The original liquid level before the cylinder is added.
- The increased liquid level indicated by \( \Delta h \) after the cylinder is placed in the tank.
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