Please answer these 2 questions. Only final answer needed. Please fast. ### Problem Statement**Scenario:**Air at standard conditions enters the compressor shown in the figure below at a rate of 10 ft³/s. It leaves the tank through a 1.2-in.-diameter pipe with a density of 0.0035 slugs/ft³ and a uniform speed of 697 ft/s.**Tasks:**(a) Determine the rate (slugs/s) at which the mass of air in the tank is increasing or decreasing.(b) Determine the average time rate of change of air density within the tank.**Figure Description:**The figure illustrates a tank with a volume of 20 ft³. Air entering the tank through a compressor has a volume flow rate of 10 ft³/s and a density of 0.00238 slugs/ft³. Air exits the tank through a pipe with a diameter of 1.2 inches at a velocity of 697 ft/s and a density of 0.0035 slugs/ft³.**Formulas:**(a) \(\frac{DM}{Dt}\) = slugs/s(b) \(\frac{D \rho}{Dt}\) = slugs/ft³·s ### Estimating Time to Fill a Cone-Shaped Container**Problem Statement:**Estimate the time required to fill with water a cone-shaped container (see the figure below) 4 ft high and 4 ft across at the top if the filling rate is 21 gal/min.**Diagram Explanation:**The provided diagram depicts a cone-shaped container being filled with water. The cone has a height and a top diameter of 4 feet each. Water is being poured into the cone through a tube.**Given Data:**- Height of the cone (h) = 4 ft- Diameter of the top of the cone = 4 ft (Radius (r) of the cone = 2 ft)- Filling rate = 21 gallons per minute**Calculation:**To determine the time required to fill the cone, we should first calculate the volume of the cone.The volume (V) of a cone is given by the formula:\[ V = \frac{1}{3}\pi r^2 h \]Substituting the given values:\[ r = 2 \text{ ft} \]\[ h = 4 \text{ ft} \]\[ V = \frac{1}{3} \pi (2)^2 (4) \]\[ V = \frac{1}{3} \pi (4)(4) \]\[ V = \frac{1}{3} \pi (16) \]\[ V = \frac{16}{3} \pi \text{ cubic feet} \]To convert the volume from cubic feet to gallons we use the conversion factor:1 cubic foot = 7.48 gallons\[ V = \frac{16}{3} \pi \times 7.48 \text{ gallons} \]\[ V \approx 125.6 \text{ gallons} \]Now, to find the time (t) to fill this volume at the rate of 21 gallons per minute:\[ t = \frac{\text{Total Volume}}{\text{Filling Rate}} \]\[ t = \frac{125.6 \text{ gallons}}{21 \text{ gallons per minute}} \]\[ t \approx 5.98 \text{ minutes} \]So, the estimated time to fill the cone-shaped container is approximately 6 minutes.**Input Area:**```t = [ ] min```This setup

Given Data Filling rate, Q=21gal/min Height, h=4ft Radius, r=2ft

Answered: Estimate the time required to fill with…

Estimate the time required to fill with water a cone shaped container (see the figure below) 4 ft high and 4 ft across at the top if the filling rate is 21 gal/min. 4ft 4ft

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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Question

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

### Problem Statement

**Scenario:**

Air at standard conditions enters the compressor shown in the figure below at a rate of 10 ft³/s. It leaves the tank through a 1.2-in.-diameter pipe with a density of 0.0035 slugs/ft³ and a uniform speed of 697 ft/s.

**Tasks:**

(a) Determine the rate (slugs/s) at which the mass of air in the tank is increasing or decreasing.

(b) Determine the average time rate of change of air density within the tank.

**Figure Description:**

The figure illustrates a tank with a volume of 20 ft³. Air entering the tank through a compressor has a volume flow rate of 10 ft³/s and a density of 0.00238 slugs/ft³. Air exits the tank through a pipe with a diameter of 1.2 inches at a velocity of 697 ft/s and a density of 0.0035 slugs/ft³.

**Formulas:**

(a) \(\frac{DM}{Dt}\) =
slugs/s

(b) \(\frac{D \rho}{Dt}\) =
slugs/ft³·s

### Estimating Time to Fill a Cone-Shaped Container

**Problem Statement:**
Estimate the time required to fill with water a cone-shaped container (see the figure below) 4 ft high and 4 ft across at the top if the filling rate is 21 gal/min.

**Diagram Explanation:**
The provided diagram depicts a cone-shaped container being filled with water. The cone has a height and a top diameter of 4 feet each. Water is being poured into the cone through a tube.

**Given Data:**
- Height of the cone (h) = 4 ft
- Diameter of the top of the cone = 4 ft (Radius (r) of the cone = 2 ft)
- Filling rate = 21 gallons per minute

**Calculation:**
To determine the time required to fill the cone, we should first calculate the volume of the cone.

The volume (V) of a cone is given by the formula:
\[ V = \frac{1}{3}\pi r^2 h \]

Substituting the given values:
\[ r = 2 \text{ ft} \]
\[ h = 4 \text{ ft} \]

\[ V = \frac{1}{3} \pi (2)^2 (4) \]
\[ V = \frac{1}{3} \pi (4)(4) \]
\[ V = \frac{1}{3} \pi (16) \]
\[ V = \frac{16}{3} \pi \text{ cubic feet} \]

To convert the volume from cubic feet to gallons we use the conversion factor:
1 cubic foot = 7.48 gallons

\[ V = \frac{16}{3} \pi \times 7.48 \text{ gallons} \]
\[ V \approx 125.6 \text{ gallons} \]

Now, to find the time (t) to fill this volume at the rate of 21 gallons per minute:
\[ t = \frac{\text{Total Volume}}{\text{Filling Rate}} \]
\[ t = \frac{125.6 \text{ gallons}}{21 \text{ gallons per minute}} \]
\[ t \approx 5.98 \text{ minutes} \]

So, the estimated time to fill the cone-shaped container is approximately 6 minutes.

**Input Area:**
```
t = [ ] min
```

This setup

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