Please answer these 2 questions. Only final answer needed. Please fast. ### Solving Sewer Backup Flooding in Your BasementStorm sewer backup can cause significant damage to your basement by flooding it steadily at a rate of 1 inch of depth per hour. Considering a basement with a floor area of 2000 square feet (ft²):### Problem StatementDetermine the pump capacity (in gallons per minute, gal/min) required to:1. **(a) Maintain a constant water level** in the basement despite the incoming backup until the issue is resolved.2. **(b) Reduce the water accumulation** in the basement by 3 inches per hour, even while the backup continues.### Solution:#### (a) Maintaining a Constant Water LevelFirst, we need to calculate the volume of water entering the basement per hour:- The basement area is 2000 ft².- The depth of water entering per hour is 1 inch. Convert the depth to feet:\[ 1 \text{ inch} = \frac{1}{12} \text{ feet} \]The volume of water in cubic feet is:\[ \text{Volume} = \text{Area} \times \text{Depth} \]\[ \text{Volume} = 2000 \, \text{ft}^2 \times \frac{1}{12} \, \text{ft} \]\[ \text{Volume} = \frac{2000}{12} \, \text{ft}^3 \]\[ \text{Volume} = 166.67 \, \text{ft}^3 \]Convert cubic feet to gallons:\[ 1 \, \text{ft}^3 = 7.48 \, \text{gallons} \]\[ \text{Volume in gallons} = 166.67 \, \text{ft}^3 \times 7.48 \, \text{gallons/ft}^3 \]\[ \text{Volume in gallons} = 1247.52 \, \text{gallons} \]The pump capacity required to keep the water at a constant level:\[ Q_{out} = \frac{1247.52 \, \text{gallons}}{60 \, \text{minutes}} \]\[ Q_{out} = 20.79 \, \text{gal/min} \]### **Answer:**\[ (a **Fluid Dynamics Problem: Merging Streams**Two rivers merge to form a larger river as shown in the figure below. At a location downstream from the junction (before the two streams completely merge), the nonuniform velocity profile is as shown and the depth is 6 ft. Determine the value of V.Assume $ V_1 = 0.77V $### Diagram ExplanationThe diagram consists of two merging streams and the resultant larger river with labeled dimensions and flow velocities.1. **Left Stream:** - Velocity: 3 ft/s - Width: 50 ft - Depth: 3 ft2. **Bottom Stream:** - Velocity: 4 ft/s - Width: 80 ft - Depth: 5 ft3. **Merged Stream:** - Nonuniform velocity profile with sections labeled $ V_1 $ and $ V $ - Widths of segments: - $ V_1 $ segments: 30 ft - $ V $ segments: 70 ft - Depth: 6 ft4. **Velocity Profile:** - $ V_1 = 0.77V $### Determine the Value of V\[ V = \] ________________ $ \text{ft/s} $Provide your answer in the box above.### Calculation ApproachTo calculate the velocity $ V $ in the merged stream:1. **Calculate Flow in Each Segment:** For the left stream: \[ Q_{\text{left}} = \text{velocity} \times \text{width} \times \text{depth} = 3 \, \text{ft/s} \times 50 \, \text{ft} \times 3 \, \text{ft} \] For the bottom stream: \[ Q_{\text{bottom}} = \text{velocity} \times \text{width} \times \text{depth} = 4 \, \text{ft/s} \times 80 \, \text{ft} \times 5 \, \text{ft} \]2. **Sum of Flows:** \[ Q_{\text{total}} = Q_{\text{left}} + Q_{\text{bottom}} \]3. **Velocity Profile in Merged Stream:** Using

Water enters during one hour=2000(1/12)=166.67 ft3 1ft3=7.48 gallon Water enters during one…

Answered: Storm sewer backup causes your basement…

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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Please answer these 2 questions. Only final answer needed. Please fast.

### Solving Sewer Backup Flooding in Your Basement

Storm sewer backup can cause significant damage to your basement by flooding it steadily at a rate of 1 inch of depth per hour. Considering a basement with a floor area of 2000 square feet (ft²):

### Problem Statement

Determine the pump capacity (in gallons per minute, gal/min) required to:

1. **(a) Maintain a constant water level** in the basement despite the incoming backup until the issue is resolved.
2. **(b) Reduce the water accumulation** in the basement by 3 inches per hour, even while the backup continues.

### Solution:

#### (a) Maintaining a Constant Water Level

First, we need to calculate the volume of water entering the basement per hour:

- The basement area is 2000 ft².
- The depth of water entering per hour is 1 inch.

Convert the depth to feet:

\[ 1 \text{ inch} = \frac{1}{12} \text{ feet} \]

The volume of water in cubic feet is:

\[ \text{Volume} = \text{Area} \times \text{Depth} \]
\[ \text{Volume} = 2000 \, \text{ft}^2 \times \frac{1}{12} \, \text{ft} \]
\[ \text{Volume} = \frac{2000}{12} \, \text{ft}^3 \]
\[ \text{Volume} = 166.67 \, \text{ft}^3 \]

Convert cubic feet to gallons:

\[ 1 \, \text{ft}^3 = 7.48 \, \text{gallons} \]
\[ \text{Volume in gallons} = 166.67 \, \text{ft}^3 \times 7.48 \, \text{gallons/ft}^3 \]
\[ \text{Volume in gallons} = 1247.52 \, \text{gallons} \]

The pump capacity required to keep the water at a constant level:

\[ Q_{out} = \frac{1247.52 \, \text{gallons}}{60 \, \text{minutes}} \]

\[ Q_{out} = 20.79 \, \text{gal/min} \]

### **Answer:**

\[ (a

$**Fluid Dynamics Problem: Merging Streams** Two rivers merge to form a larger river as shown in the figure below. At a location downstream from the junction (before the two streams completely merge), the nonuniform velocity profile is as shown and the depth is 6 ft. Determine the value of V. Assume $ V_1 = 0.77V $ ### Diagram Explanation The diagram consists of two merging streams and the resultant larger river with labeled dimensions and flow velocities. 1. **Left Stream:** - Velocity: 3 ft/s - Width: 50 ft - Depth: 3 ft 2. **Bottom Stream:** - Velocity: 4 ft/s - Width: 80 ft - Depth: 5 ft 3. **Merged Stream:** - Nonuniform velocity profile with sections labeled $ V_1 $ and $ V $ - Widths of segments: - $ V_1 $ segments: 30 ft - $ V $ segments: 70 ft - Depth: 6 ft 4. **Velocity Profile:** - $ V_1 = 0.77V $ ### Determine the Value of V \[ V = \] ________________ $ \text{ft/s} $ Provide your answer in the box above. ### Calculation Approach To calculate the velocity $ V $ in the merged stream: 1. **Calculate Flow in Each Segment:** For the left stream: \[ Q_{\text{left}} = \text{velocity} \times \text{width} \times \text{depth} = 3 \, \text{ft/s} \times 50 \, \text{ft} \times 3 \, \text{ft} \] For the bottom stream: \[ Q_{\text{bottom}} = \text{velocity} \times \text{width} \times \text{depth} = 4 \, \text{ft/s} \times 80 \, \text{ft} \times 5 \, \text{ft} \] 2. **Sum of Flows:** \[ Q_{\text{total}} = Q_{\text{left}} + Q_{\text{bottom}} \] 3. **Velocity Profile in Merged Stream:** Using$

Transcribed Image Text:**Fluid Dynamics Problem: Merging Streams** Two rivers merge to form a larger river as shown in the figure below. At a location downstream from the junction (before the two streams completely merge), the nonuniform velocity profile is as shown and the depth is 6 ft. Determine the value of V. Assume $ V_1 = 0.77V $ ### Diagram Explanation The diagram consists of two merging streams and the resultant larger river with labeled dimensions and flow velocities. 1. **Left Stream:** - Velocity: 3 ft/s - Width: 50 ft - Depth: 3 ft 2. **Bottom Stream:** - Velocity: 4 ft/s - Width: 80 ft - Depth: 5 ft 3. **Merged Stream:** - Nonuniform velocity profile with sections labeled $ V_1 $ and $ V $ - Widths of segments: - $ V_1 $ segments: 30 ft - $ V $ segments: 70 ft - Depth: 6 ft 4. **Velocity Profile:** - $ V_1 = 0.77V $ ### Determine the Value of V \[ V = \] ________________ $ \text{ft/s} $ Provide your answer in the box above. ### Calculation Approach To calculate the velocity $ V $ in the merged stream: 1. **Calculate Flow in Each Segment:** For the left stream: \[ Q_{\text{left}} = \text{velocity} \times \text{width} \times \text{depth} = 3 \, \text{ft/s} \times 50 \, \text{ft} \times 3 \, \text{ft} \] For the bottom stream: \[ Q_{\text{bottom}} = \text{velocity} \times \text{width} \times \text{depth} = 4 \, \text{ft/s} \times 80 \, \text{ft} \times 5 \, \text{ft} \] 2. **Sum of Flows:** \[ Q_{\text{total}} = Q_{\text{left}} + Q_{\text{bottom}} \] 3. **Velocity Profile in Merged Stream:** Using

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