An irrigation system allows water to flow in the pattern shown in the figure below. Water flows into the system at A and exits at B,C, D and E with the amounts shown. Using the fact that at each point the water entering equals the water leaving, formulate an equation for water flow at each of the five points and solve the system for the five variables which represent the amounts of water flow.Using RREF The image displays a network flow diagram involving four nodes labeled A, B, C, D, and E. The flow of liquid, measured in gallons per hour (gal/hr), is indicated between these nodes with specific arrows and flow values. The system is described as follows:- **Input**: 500,000 gal/hr enters at node A.- **Node A**: - Flow splits into two branches: - $ x_1 $ directed towards node B. - $ x_2 $ directed towards node C.- **Node B**: - Receives flow $ x_1 $ from node A. - Flow splits into two branches and one output: - $ x_4 $ directed towards node D. - $ x_5 $ directed towards node E. - Output: 50,000 gal/hr exits.- **Node C**: - Receives flow from $ x_2 $ from node A. - $ x_2 $ becomes $ x_3 $ leading towards node D. - Output: 50,000 gal/hr exits.- **Node D**: - Receives flow from nodes B ($ x_4 $) and C ($ x_3 $). - Output: 200,000 gal/hr exits.- **Node E**: - Receives flow $ x_5 $ from node B. - Output: 200,000 gal/hr exits.Each node redistributes the incoming flow according to the indicated paths, with specific outputs defined. The diagram represents a dynamic system of fluid distribution with specified inflow and outflow rates, subject to conservation of mass at each node.

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Answered: An irrigation system allows water to…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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An irrigation system allows water to flow in the pattern shown in the figure below. Water flows into the system at A and exits at B,C, D and E with the amounts shown. Using the fact that at each point the water entering equals the water leaving, formulate an equation for water flow at each of the five points and solve the system for the five variables which represent the amounts of water flow.

Using RREF

The image displays a network flow diagram involving four nodes labeled A, B, C, D, and E. The flow of liquid, measured in gallons per hour (gal/hr), is indicated between these nodes with specific arrows and flow values. The system is described as follows:

- **Input**: 500,000 gal/hr enters at node A.
- **Node A**:
- Flow splits into two branches:
- $ x_1 $ directed towards node B.
- $ x_2 $ directed towards node C.

- **Node B**:
- Receives flow $ x_1 $ from node A.
- Flow splits into two branches and one output:
- $ x_4 $ directed towards node D.
- $ x_5 $ directed towards node E.
- Output: 50,000 gal/hr exits.

- **Node C**:
- Receives flow from $ x_2 $ from node A.
- $ x_2 $ becomes $ x_3 $ leading towards node D.
- Output: 50,000 gal/hr exits.

- **Node D**:
- Receives flow from nodes B ($ x_4 $) and C ($ x_3 $).
- Output: 200,000 gal/hr exits.

- **Node E**:
- Receives flow $ x_5 $ from node B.
- Output: 200,000 gal/hr exits.

Each node redistributes the incoming flow according to the indicated paths, with specific outputs defined. The diagram represents a dynamic system of fluid distribution with specified inflow and outflow rates, subject to conservation of mass at each node.

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