Water flows steadily from the large open tank as shown in the figure. if viscous effects are negligible determine a) the flowrate, Q, in M^3/s b)The manometer reading, h, in m.
Water flows steadily from the large open tank as shown in the figure. if viscous effects are negligible determine a) the flowrate, Q, in M^3/s b)The manometer reading, h, in m.
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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Fluid
Water flows steadily from the large open tank as shown in the figure. if viscous effects are negligible determine
a) the flowrate, Q, in M^3/s
b)The manometer reading, h, in m.
![### Flow Rate Determination in a Water Tank System
This illustration depicts a water tank system designed to determine the flow rate \( Q \) from a large water tank through a horizontal pipe. Below is a detailed description of the key features and dimensions of the system:
#### Diagram Elements:
1. **Large Water Tank**:
- Contains water with a labeled height of **6 meters** (marked with a vertical double-headed arrow on the right side of the tank and indicated as "water").
- This tank is static and supplies water to the connected system.
2. **Connected Pipes**:
- **Horizontal Pipe**:
- Located on the left side of the tank, it has two distinctly marked sections:
- **First Segment**:
- Length: Corresponding to a diameter of **0.15 meters (15 cm)**.
- This segment leads into a narrower segment of the pipe.
- **Second Segment**:
- Length: Corresponding to a diameter of **0.05 meters (5 cm)**.
- Connects to the base of a vertical riser pipe.
3. **Vertical Riser Pipe**:
- Extends vertically upward from the horizontal pipe.
- The height of the water column in the riser is unknown and labeled as \( h \), denoted by a red double-headed arrow.
4. **Flow Rate Determination**:
- The flow rate \( Q \) of water through the system is the primary unknown parameter to be calculated.
- It is represented near the exit of the pipe on the left side, indicated with a question mark next to \( Q \).
### Explanation of Process:
The system operates on the principle of fluid dynamics, considering factors such as the tank's height (water pressure due to gravity) and the pipe dimensions. By applying Bernoulli's equation and principles for fluid flow:
- **Bernoulli’s Equation**:
\[
P_1 + \frac{1}{2}\rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho g h_2
\]
Here, \( \rho \) is the fluid density, \( v \) is fluid velocity, \( g \) is the acceleration due to gravity, and \( h \) is the height of water.
- **Continuity Equation](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb738ee4b-0d92-438d-b96f-d8d02fb325c0%2F7c71968f-169c-4e3c-919c-e615ee1fca1b%2F148z6wi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Flow Rate Determination in a Water Tank System
This illustration depicts a water tank system designed to determine the flow rate \( Q \) from a large water tank through a horizontal pipe. Below is a detailed description of the key features and dimensions of the system:
#### Diagram Elements:
1. **Large Water Tank**:
- Contains water with a labeled height of **6 meters** (marked with a vertical double-headed arrow on the right side of the tank and indicated as "water").
- This tank is static and supplies water to the connected system.
2. **Connected Pipes**:
- **Horizontal Pipe**:
- Located on the left side of the tank, it has two distinctly marked sections:
- **First Segment**:
- Length: Corresponding to a diameter of **0.15 meters (15 cm)**.
- This segment leads into a narrower segment of the pipe.
- **Second Segment**:
- Length: Corresponding to a diameter of **0.05 meters (5 cm)**.
- Connects to the base of a vertical riser pipe.
3. **Vertical Riser Pipe**:
- Extends vertically upward from the horizontal pipe.
- The height of the water column in the riser is unknown and labeled as \( h \), denoted by a red double-headed arrow.
4. **Flow Rate Determination**:
- The flow rate \( Q \) of water through the system is the primary unknown parameter to be calculated.
- It is represented near the exit of the pipe on the left side, indicated with a question mark next to \( Q \).
### Explanation of Process:
The system operates on the principle of fluid dynamics, considering factors such as the tank's height (water pressure due to gravity) and the pipe dimensions. By applying Bernoulli's equation and principles for fluid flow:
- **Bernoulli’s Equation**:
\[
P_1 + \frac{1}{2}\rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho g h_2
\]
Here, \( \rho \) is the fluid density, \( v \) is fluid velocity, \( g \) is the acceleration due to gravity, and \( h \) is the height of water.
- **Continuity Equation
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