block slide down

logistic_guy

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Apr 17, 2024
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here is the question

A block slides down a long, straight, inclined wall at speed \(\displaystyle V\), riding on a thin film of oil of thickness \(\displaystyle h\) as shown. The weight of the block is \(\displaystyle W\), and its surface area in contact with the oil film is \(\displaystyle A\). Suppose \(\displaystyle V\) is measured, and \(\displaystyle W, A, \) angle \(\displaystyle \alpha,\) and viscosity \(\displaystyle \mu\) are also known. Oil film thickness \(\displaystyle h\) is not known. Generate an exact analytical expression for \(\displaystyle h\) as a function of the known parameters, \(\displaystyle V, A, W, \alpha, \) and \(\displaystyle \mu\).

block.png


my attemb
i assume force of gravity pulling block down and i also assume tiny friction force in the opposite side
\(\displaystyle W\sin \alpha - F_{r} = ma\)
this question is written very bad. it don't tell me if there is friction. it also don't tell me if speed constant or change😕
i'll assume there is no acceleration
\(\displaystyle W\sin \alpha - F_{r} = 0\)
this expression tell me speed and surface area and viscosity is part of friction
from previous lesson i remember speed and viscosity and oil thickness is part of shear stress in Couette flow
but in quesition it don't tell anything about shear stress or Couette flow
do i have to assume this or i'm wrong?☹️
very bad author, it write poorly question for advance engineering
 
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