diameter pipe with a density of 0.0035 slugs/ft³ and a uniform speed of 696 ft/s. (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. Compressor 10 ft³/s - 0.00238 slugs/ft³ (a) (b) DM Dt Dp Dt i i Tank volume 20 ft³ 1.2 in. slugs/s slugs/ft³.s 696ft/s 0.0035 slugs/ft³

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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**Problem Description:**

Air at standard conditions enters the compressor shown in the figure at a rate of 10 ft³/s. It exits the tank through a 1.2-inch diameter pipe with a density of 0.0035 slugs/ft³ and a uniform speed of 696 ft/s.

(a) **Mass Flow Rate Calculation:**

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

(b) **Density Rate of Change Calculation:**

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

---

**Diagram Explanation:**

- **Compressor System:** The system includes a tank with a volume of 20 ft³.
  
- **Inflow:** Air enters the compressor at a flow rate of 10 ft³/s with a density of 0.00238 slugs/ft³.

- **Outflow:** Air exits through a pipe with a speed of 696 ft/s and a density of 0.0035 slugs/ft³.

- **Pipe Diameter:** The pipe has a diameter of 1.2 inches.

---

**Equations:**

(a) \(\frac{DM}{Dt} = \) [Input field for slugs/s]

(b) \(\frac{D\rho}{Dt} = \) [Input field for slugs/ft³·s]

---

Use these details to complete the calculations for both mass flow rate and density change rate.
Transcribed Image Text:**Problem Description:** Air at standard conditions enters the compressor shown in the figure at a rate of 10 ft³/s. It exits the tank through a 1.2-inch diameter pipe with a density of 0.0035 slugs/ft³ and a uniform speed of 696 ft/s. (a) **Mass Flow Rate Calculation:** Determine the rate (in slugs/s) at which the mass of air in the tank is either increasing or decreasing. (b) **Density Rate of Change Calculation:** Determine the average time rate of change of air density within the tank. --- **Diagram Explanation:** - **Compressor System:** The system includes a tank with a volume of 20 ft³. - **Inflow:** Air enters the compressor at a flow rate of 10 ft³/s with a density of 0.00238 slugs/ft³. - **Outflow:** Air exits through a pipe with a speed of 696 ft/s and a density of 0.0035 slugs/ft³. - **Pipe Diameter:** The pipe has a diameter of 1.2 inches. --- **Equations:** (a) \(\frac{DM}{Dt} = \) [Input field for slugs/s] (b) \(\frac{D\rho}{Dt} = \) [Input field for slugs/ft³·s] --- Use these details to complete the calculations for both mass flow rate and density change rate.
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