Consider a reducer with inlet and outlet diameters of D1 and D2, respectively. The respective velocities are U1 and U2, as shown below. The fluid of density, ρ exits at an angle θ with respect to the horizontal plane. The input is along the horizontal plane. Assume no viscous effects, i.e., μ = 0. Calculate the (i) vertical, and (ii) horizontal forces to hold the reducer stationary. Consider the following: • Mass balance • Energy balance • Momentum balance in horizontal direction • Momentum balance in vertical direction The image depicts a fluid dynamics diagram illustrating the flow through an elbow pipe.- **Flow Direction**: The flow enters with velocity \( U_1 \) in a horizontal direction and exits with velocity \( U_2 \) at an angle \( \theta \).- **Pipe Dimensions**: - \( D_1 \): Diameter of the pipe at the inlet. - \( D_2 \): Diameter of the pipe at the outlet.- **Force Components**: - \( F_H \): Horizontal force component. - \( F_V \): Vertical force component.- **Angle of Deflection**: The angle \( \theta \) indicates the deflection of flow at the outlet compared to the inlet. This diagram serves to visualize the alteration in flow direction and velocity as fluid moves through the elbow, and the resulting forces that develop from this change.

Law of conservation of momentum: According to this law, " the rate of change of linear momentum of…

Answered: Consider a reducer with inlet and…

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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Consider a reducer with inlet and outlet diameters of D1 and D2, respectively. The respective
velocities are U1 and U2, as shown below. The fluid of density, ρ exits at an angle θ with respect
to the horizontal plane. The input is along the horizontal plane. Assume no viscous effects, i.e., μ
= 0.
Calculate the (i) vertical, and (ii) horizontal forces to hold the reducer stationary.
Consider the following:
• Mass balance
• Energy balance
• Momentum balance in horizontal direction
• Momentum balance in vertical direction

The image depicts a fluid dynamics diagram illustrating the flow through an elbow pipe.

- **Flow Direction**: The flow enters with velocity \( U_1 \) in a horizontal direction and exits with velocity \( U_2 \) at an angle \( \theta \).

- **Pipe Dimensions**:
- \( D_1 \): Diameter of the pipe at the inlet.
- \( D_2 \): Diameter of the pipe at the outlet.

- **Force Components**:
- \( F_H \): Horizontal force component.
- \( F_V \): Vertical force component.

- **Angle of Deflection**: The angle \( \theta \) indicates the deflection of flow at the outlet compared to the inlet.

This diagram serves to visualize the alteration in flow direction and velocity as fluid moves through the elbow, and the resulting forces that develop from this change.

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