The velocity of air in the diverging pipe shown in the figure below is given by V1 = 14t ft/s and V2 = 10t ft/s, where t is in seconds. Determine (a) the local acceleration at point (1); (b) the local acceleration at point (2). (1) (2) (a) i ft/s2 (b) i ft/s2

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### Air Velocity in a Diverging Pipe: Local Acceleration

The velocity of air in a diverging pipe is illustrated in the following figure. The given velocities are V₁ (at point 1) and V₂ (at point 2) where:

- \( V_1 = 14 \, \text{ft/s} \)
- \( V_2 = 10 \, \text{ft/s} \)

(Note that time \( t \) is in seconds.)

#### Task:
Determine:
(a) The local acceleration at point (1);
(b) The local acceleration at point (2).

The diverging pipe diagram is as follows:
- **Point (1)**: Located at the narrow inlet of the pipe, where the velocity of air is \( V_1 \).
- **Point (2)**: Located at the wider outlet of the pipe, where the velocity of air is \( V_2 \).

The diagram shows a diverging pipe with:
- Arrows indicating the direction of air flow.
- Velocity \( V_1 \) entering the narrow end.
- Velocity \( V_2 \) leaving the wider end.

### Diagram Explanation:
- **Left Point (1)**: Air enters with velocity \( V_1 = 14 \, \text{ft/s} \).
- **Right Point (2)**: Air exits with velocity \( V_2 = 10 \, \text{ft/s} \).

### Solution:
Please input the local acceleration values based on your calculations:

- (a) \( \boxed{} \, \text{ft/s}^2 \)
- (b) \( \boxed{} \, \text{ft/s}^2 \)

---

Provide your results in the text boxes for:
- Local acceleration at point (1).
- Local acceleration at point (2).
Transcribed Image Text:### Air Velocity in a Diverging Pipe: Local Acceleration The velocity of air in a diverging pipe is illustrated in the following figure. The given velocities are V₁ (at point 1) and V₂ (at point 2) where: - \( V_1 = 14 \, \text{ft/s} \) - \( V_2 = 10 \, \text{ft/s} \) (Note that time \( t \) is in seconds.) #### Task: Determine: (a) The local acceleration at point (1); (b) The local acceleration at point (2). The diverging pipe diagram is as follows: - **Point (1)**: Located at the narrow inlet of the pipe, where the velocity of air is \( V_1 \). - **Point (2)**: Located at the wider outlet of the pipe, where the velocity of air is \( V_2 \). The diagram shows a diverging pipe with: - Arrows indicating the direction of air flow. - Velocity \( V_1 \) entering the narrow end. - Velocity \( V_2 \) leaving the wider end. ### Diagram Explanation: - **Left Point (1)**: Air enters with velocity \( V_1 = 14 \, \text{ft/s} \). - **Right Point (2)**: Air exits with velocity \( V_2 = 10 \, \text{ft/s} \). ### Solution: Please input the local acceleration values based on your calculations: - (a) \( \boxed{} \, \text{ft/s}^2 \) - (b) \( \boxed{} \, \text{ft/s}^2 \) --- Provide your results in the text boxes for: - Local acceleration at point (1). - Local acceleration at point (2).
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