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
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
Chapter2: Loads On Structures
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
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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