Answered: Required information Oil flow in a…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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$### Required Information Oil flow in a journal bearing can be treated as parallel flow between two large isothermal plates with one plate moving at a constant velocity of 5 m/s and the other stationary. Consider such a flow with a uniform spacing of 0.5 mm between the plates. The temperatures of the upper and lower plates are 40°C and 15°C, respectively. **NOTE:** This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. **Diagram Explanation:** The diagram shows a flow between two parallel plates. The top plate is moving at a velocity of $ V \, m/s $ to the right, while the bottom plate is stationary. The velocity profile $ u(y) $ indicates the flow direction and distribution between the plates. The properties of oil at the average temperature of (40+15)/2 = 27.5°C are: - $ k = 0.145 \, \text{W/m·K} $ - $ \mu = 0.605 \, \text{kg/m·s} = 0.605 \, \text{N·s/m}^2 $ --- By simplifying and solving the continuity, momentum, and energy equations, determine the maximum temperature and where it occurs. - *The maximum temperature is* $ 337.32 \, °C $. (Incorrect) - *The location of the maximum temperature is* $ 0.369 \, \text{mm above the bottom plate} $. (Correct)$

Transcribed Image Text:### Required Information Oil flow in a journal bearing can be treated as parallel flow between two large isothermal plates with one plate moving at a constant velocity of 5 m/s and the other stationary. Consider such a flow with a uniform spacing of 0.5 mm between the plates. The temperatures of the upper and lower plates are 40°C and 15°C, respectively. **NOTE:** This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. **Diagram Explanation:** The diagram shows a flow between two parallel plates. The top plate is moving at a velocity of $ V \, m/s $ to the right, while the bottom plate is stationary. The velocity profile $ u(y) $ indicates the flow direction and distribution between the plates. The properties of oil at the average temperature of (40+15)/2 = 27.5°C are: - $ k = 0.145 \, \text{W/m·K} $ - $ \mu = 0.605 \, \text{kg/m·s} = 0.605 \, \text{N·s/m}^2 $ --- By simplifying and solving the continuity, momentum, and energy equations, determine the maximum temperature and where it occurs. - *The maximum temperature is* $ 337.32 \, °C $. (Incorrect) - *The location of the maximum temperature is* $ 0.369 \, \text{mm above the bottom plate} $. (Correct)

Expert Solution

Step 1

Given:

Velocity, v = 5 m/s

spacing, L = 0.5 mm

Temperature at the top plate, T_top = 40^oC

Temperature at the bottom plate, T_bot = 15^oC

Average temperature = 27.5^oC

k = 0.145 W/m.K

$μ$ = 0.605 N.s/m²

To find:

Maximum temperature

Distance where maximum temperature occurs

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