We were discussing the basic concept of kinetic energy correction factor and momentum correction factor and power absorbed in viscous flow, in the subject of fluid mechanics, in our recent posts.
Now we will go ahead to find out the power required to overcome the viscous resistance of journal bearings, in the subject of fluid mechanics, with the help of this post.
Power required to overcome the viscous resistance of journal bearings
Let us consider that a shaft is rotating in a journal bearing. Let us think that oil is used as lubricant in order to fill the clearance between the shaft and journal bearing.
When shaft will be rotated, oil film in contact with the shaft will also be rotated along with shaft. Oil film in contact with the shaft will be rotated with the similar speed with which shaft will be rotated.
While, oil film in contact with the journal bearing will not be rotated i.e. oil film in contact with the journal bearing will be stationary. Therefore oil will offer the viscous resistance to the rotating shaft.
Let us consider the following data from above figure of journal bearing and shaft.
N = Speed of shaft in rpm
D = Diameter of rotating shaft
L = Length of oil film
t = Thickness of oil film
τ = Shear stress in the oil
V = Tangential speed of the shaft
ω = Angular speed of the shaft
We will have following expression for the angular speed of shaft and tangential speed of the shaft as mentioned here.
ω = 2ПN/60
V = R x ω = (D/2) x ω
V = (D/2) x 2ПN/60
V = ПDN/60
τ = Shear stress in the oil = μ x du/dy
Now we will go ahead to start a new topic in the subject of fluid mechanics i.e. power requirement to overcome the viscous resistance of foot-step bearings.
Do you have any suggestions? Please write in comment box.
Reference:
Fluid mechanics, By R. K. Bansal
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