**Educational Content: Conservation of Mass in Fluid Dynamics**### Task 1.3: Find the Outlet Velocity#### Visual Explanation:The image shows three different configurations of circular tubes. Each case presents a different scenario for analyzing fluid flow while maintaining the principle of conservation of mass. The inlet velocity for all cases is given as 1 cm/s.#### Case Descriptions:- **Case 1:** - The tube starts with a diameter of 4 mm and narrows to a diameter of 2 mm. - This configuration demonstrates a contraction as the fluid moves through the tube.- **Case 2:** - Similar to Case 1, the tube starts with a diameter of 4 mm, narrows to 2 mm, but includes a horizontal section with a consistent diameter of 4 mm. - This setup shows a contraction with an additional path extension before narrowing.- **Case 3:** - The tube starts and ends with a diameter of 4 mm but expands to a diameter of 8 mm at the middle section. - This case illustrates both contraction and expansion within the same system.#### Objective:Determine the outlet velocity for each configuration by applying the conservation of mass principle, assuming steady, incompressible flow. The continuity equation for incompressible fluids is used: \[ A_1 \cdot V_1 = A_2 \cdot V_2 \]where \( A \) is the cross-sectional area and \( V \) is the velocity of the fluid.**Note:** Ensure to calculate the area using the formula for the area of a circle \( A = \pi \left(\frac{d}{2}\right)^2 \) where \( d \) is the diameter.This exercise emphasizes the application of fundamental fluid dynamics concepts and analytical skills to solve real-world engineering problems.

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Case 1 1.3. dia=4 mm dia=2 mm dia=4 mm V Case 2 dia=2 mm, X 14 mm Case 3 dia=4 mm dia=8 mm dia=4 mm Conservation of Mass: Find the velocity of the flow at the outlet for each of the 3 circular tubes shown. Inlet velocity is 1 cm/s for all cases.

Case 1 1.3. dia=4 mm dia=2 mm dia=4 mm V Case 2 dia=2 mm, X 14 mm Case 3 dia=4 mm dia=8 mm dia=4 mm Conservation of Mass: Find the velocity of the flow at the outlet for each of the 3 circular tubes shown. Inlet velocity is 1 cm/s for all cases.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Applied Fluid Mechanics

A fluid is a substance that is continuously deformed by the application of shear stress. The rate of deformation of a fluid depends on its viscosity. The fluid tries to flow when it interacts with some other system.

Question

**Educational Content: Conservation of Mass in Fluid Dynamics**

### Task 1.3: Find the Outlet Velocity

#### Visual Explanation:
The image shows three different configurations of circular tubes. Each case presents a different scenario for analyzing fluid flow while maintaining the principle of conservation of mass. The inlet velocity for all cases is given as 1 cm/s.

#### Case Descriptions:

- **Case 1:**
- The tube starts with a diameter of 4 mm and narrows to a diameter of 2 mm.
- This configuration demonstrates a contraction as the fluid moves through the tube.

- **Case 2:**
- Similar to Case 1, the tube starts with a diameter of 4 mm, narrows to 2 mm, but includes a horizontal section with a consistent diameter of 4 mm.
- This setup shows a contraction with an additional path extension before narrowing.

- **Case 3:**
- The tube starts and ends with a diameter of 4 mm but expands to a diameter of 8 mm at the middle section.
- This case illustrates both contraction and expansion within the same system.

#### Objective:
Determine the outlet velocity for each configuration by applying the conservation of mass principle, assuming steady, incompressible flow. The continuity equation for incompressible fluids is used:

\[ A_1 \cdot V_1 = A_2 \cdot V_2 \]

where \( A \) is the cross-sectional area and \( V \) is the velocity of the fluid.

**Note:** Ensure to calculate the area using the formula for the area of a circle \( A = \pi \left(\frac{d}{2}\right)^2 \) where \( d \) is the diameter.

This exercise emphasizes the application of fundamental fluid dynamics concepts and analytical skills to solve real-world engineering problems.

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