Find the difference between the pressure ? PA- P, = ? TAKE // h = 2 m , h2 = 4 m, h 3m (Pwater = 1000 Kg/m), (Pmercury = 13600 Kg/m²),(Pon = 850 Kg/m2) Water Mercury Oil
Find the difference between the pressure ? PA- P, = ? TAKE // h = 2 m , h2 = 4 m, h 3m (Pwater = 1000 Kg/m), (Pmercury = 13600 Kg/m²),(Pon = 850 Kg/m2) Water Mercury Oil
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Finding the Difference Between Pressures:**
**Problem Statement:**
Determine the difference in pressures between points \( A \) and \( B \).
\[ P_A - P_B = ? \]
**Given Data:**
- Heights:
- \( h_1 = 2 \, \text{m} \)
- \( h_2 = 4 \, \text{m} \)
- \( h_3 = 3 \, \text{m} \)
- Densities:
- \( \rho_{\text{water}} = 1000 \, \text{kg/m}^3 \)
- \( \rho_{\text{mercury}} = 13600 \, \text{kg/m}^3 \)
- \( \rho_{\text{oil}} = 850 \, \text{kg/m}^3 \)
**Diagram Explanation:**
The provided diagram illustrates a U-shaped tube filled with three different fluids: water, mercury, and oil. The tube is segmented into different sections labeled with respective height measurements.
1. The left arm of the tube contains water up to height \( h_1 \).
2. The middle section consists of mercury, with the topmost level reaching height \( h_2 \).
3. The right arm contains oil up to height \( h_3 \).
- Point \( A \) is marked in the water section.
- Point \( B \) is marked in the oil section.
To solve for the pressure difference \( P_A - P_B \), the concept of fluid statics and the principles of hydrostatic pressure will be used.
Hydrostatic pressure is given by:
\[ P = \rho \cdot g \cdot h \]
where:
- \( \rho \) is the fluid density,
- \( g \) is the acceleration due to gravity (approx. \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height of the fluid column.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F262066d6-857e-4a0c-85f2-e694e7155faa%2F860b074f-5462-41e8-b042-ef29c992f0f1%2F56lyf5b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Difference Between Pressures:**
**Problem Statement:**
Determine the difference in pressures between points \( A \) and \( B \).
\[ P_A - P_B = ? \]
**Given Data:**
- Heights:
- \( h_1 = 2 \, \text{m} \)
- \( h_2 = 4 \, \text{m} \)
- \( h_3 = 3 \, \text{m} \)
- Densities:
- \( \rho_{\text{water}} = 1000 \, \text{kg/m}^3 \)
- \( \rho_{\text{mercury}} = 13600 \, \text{kg/m}^3 \)
- \( \rho_{\text{oil}} = 850 \, \text{kg/m}^3 \)
**Diagram Explanation:**
The provided diagram illustrates a U-shaped tube filled with three different fluids: water, mercury, and oil. The tube is segmented into different sections labeled with respective height measurements.
1. The left arm of the tube contains water up to height \( h_1 \).
2. The middle section consists of mercury, with the topmost level reaching height \( h_2 \).
3. The right arm contains oil up to height \( h_3 \).
- Point \( A \) is marked in the water section.
- Point \( B \) is marked in the oil section.
To solve for the pressure difference \( P_A - P_B \), the concept of fluid statics and the principles of hydrostatic pressure will be used.
Hydrostatic pressure is given by:
\[ P = \rho \cdot g \cdot h \]
where:
- \( \rho \) is the fluid density,
- \( g \) is the acceleration due to gravity (approx. \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height of the fluid column.
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