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 V\displaystyle V, riding on a thin film of oil of thickness h\displaystyle h as shown. The weight of the block is W\displaystyle W, and its surface area in contact with the oil film is A\displaystyle A. Suppose V\displaystyle V is measured, and W,A,\displaystyle W, A, angle α,\displaystyle \alpha, and viscosity μ\displaystyle \mu are also known. Oil film thickness h\displaystyle h is not known. Generate an exact analytical expression for h\displaystyle h as a function of the known parameters, V,A,W,α,\displaystyle V, A, W, \alpha, and μ\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
WsinαFr=ma\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
WsinαFr=0\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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