2. a. Find the expression for dh dt dh b. Compute if D₁ = 1in, D₂ = 3 in, dt V₁ = 3ft/s, V₂ = 2ft/s, At = 2ft², T = 20°C le h At Pa Pw H
2. a. Find the expression for dh dt dh b. Compute if D₁ = 1in, D₂ = 3 in, dt V₁ = 3ft/s, V₂ = 2ft/s, At = 2ft², T = 20°C le h At Pa Pw H
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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![### Problem 2
#### a. Find the expression for \(\frac{dh}{dt}\)
#### b. Compute \(\frac{dh}{dt}\) if \(D_1 = 1\, \text{in}\), \(D_2 = 3\, \text{in}\),
\[V_1 = 3\, \text{ft/s}, \quad V_2 = 2\, \text{ft/s}, \quad A_t = 2\, \text{ft}^2, \quad T = 20^\circ C\]
### Diagram Explanation
The diagram on the right depicts a vertical tank with an inflow and outflow pipe. It illustrates the following components:
- **Inflow (1)**: Water enters the tank, indicated by the blue arrow on the left. The diameter of this inflow pipe is represented by \(D_1\).
- **Outflow (2)**: Water exits the tank, shown by the blue arrow on the right. The diameter of this outflow pipe is \(D_2\).
- **Tank**: The tank has a cross-sectional area \(A_t\).
- **Water Levels**:
- \(\rho_w\): Water density.
- \(\rho_a\): Air density (above the water level).
- **Heights**:
- \(h\): Current height of the water in the tank.
- \(H\): Total height of the tank.
The problem involves calculating the rate of change of the height (\(h\)) of water in the tank over time, considering the given inflow and outflow velocities, and specific diameters for the pipes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ce8b870-93ef-497a-8c2a-bbbd1041dd5b%2F21f7c363-ac04-4b57-b709-ef470df21056%2F6xukkq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 2
#### a. Find the expression for \(\frac{dh}{dt}\)
#### b. Compute \(\frac{dh}{dt}\) if \(D_1 = 1\, \text{in}\), \(D_2 = 3\, \text{in}\),
\[V_1 = 3\, \text{ft/s}, \quad V_2 = 2\, \text{ft/s}, \quad A_t = 2\, \text{ft}^2, \quad T = 20^\circ C\]
### Diagram Explanation
The diagram on the right depicts a vertical tank with an inflow and outflow pipe. It illustrates the following components:
- **Inflow (1)**: Water enters the tank, indicated by the blue arrow on the left. The diameter of this inflow pipe is represented by \(D_1\).
- **Outflow (2)**: Water exits the tank, shown by the blue arrow on the right. The diameter of this outflow pipe is \(D_2\).
- **Tank**: The tank has a cross-sectional area \(A_t\).
- **Water Levels**:
- \(\rho_w\): Water density.
- \(\rho_a\): Air density (above the water level).
- **Heights**:
- \(h\): Current height of the water in the tank.
- \(H\): Total height of the tank.
The problem involves calculating the rate of change of the height (\(h\)) of water in the tank over time, considering the given inflow and outflow velocities, and specific diameters for the pipes.
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