8. (cubic feet per minute) of air at 70°F at sea level. Determine (a) the force required to hold the fan and (b) the minimum power input required for the fan. Choose the control volume sufficiently large to contain the fan, and the gage pressure and the air velocity on the inlet side to be zero. Assume air approaches the fan through a large area with negligible veloc- ity and air exits the fan with a uniform velocity at atmos- pheric pressure through an imaginary cylinder whose diame- ter is the fan blade diameter. A fan with 24-in-diameter blades moves 2000 cfm 2000 cfm Fan 2 24 in

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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**Problem Statement:**

A fan with 24-inch-diameter blades moves 2000 cfm (cubic feet per minute) of air at 70°F at sea level. Determine (a) the force required to hold the fan and (b) the minimum power input required for the fan. Choose the control volume sufficiently large to contain the fan, and the gage pressure and air velocity on the inlet side to be zero. Assume air approaches the fan through a large area with negligible velocity and air exits the fan with a uniform velocity at atmospheric pressure through an imaginary cylinder whose diameter is the fan blade diameter.

**Diagram Description:**

The accompanying diagram shows a side view of the fan assembly. 

- **Direction of Airflow:** Arrows point towards and away from the fan, indicating the air entering and leaving the fan. The airflow rate is 2000 cfm.
  
- **Fan Blades:** Two fan blades are depicted, each perpendicular to the flow direction. The diameter of the fan and the imaginary exit cylinder is 24 inches.

- **Control Volume:** Shown as a rectangular boundary encompassing the fan, this is the volume within which the analysis of forces and power will be conducted.
  
- **Labels:**
  - Inlet side (1): Air enters with initial conditions of zero gauge pressure and negligible velocity.
  - Outlet side (2): Air exits with a uniform velocity at atmospheric pressure through the cylindrical section with the diameter of the fan blades. 

This diagram aids in visualizing the airflow through the fan and is essential for performing calculations in fluid dynamics.
Transcribed Image Text:**Problem Statement:** A fan with 24-inch-diameter blades moves 2000 cfm (cubic feet per minute) of air at 70°F at sea level. Determine (a) the force required to hold the fan and (b) the minimum power input required for the fan. Choose the control volume sufficiently large to contain the fan, and the gage pressure and air velocity on the inlet side to be zero. Assume air approaches the fan through a large area with negligible velocity and air exits the fan with a uniform velocity at atmospheric pressure through an imaginary cylinder whose diameter is the fan blade diameter. **Diagram Description:** The accompanying diagram shows a side view of the fan assembly. - **Direction of Airflow:** Arrows point towards and away from the fan, indicating the air entering and leaving the fan. The airflow rate is 2000 cfm. - **Fan Blades:** Two fan blades are depicted, each perpendicular to the flow direction. The diameter of the fan and the imaginary exit cylinder is 24 inches. - **Control Volume:** Shown as a rectangular boundary encompassing the fan, this is the volume within which the analysis of forces and power will be conducted. - **Labels:** - Inlet side (1): Air enters with initial conditions of zero gauge pressure and negligible velocity. - Outlet side (2): Air exits with a uniform velocity at atmospheric pressure through the cylindrical section with the diameter of the fan blades. This diagram aids in visualizing the airflow through the fan and is essential for performing calculations in fluid dynamics.
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