# Analysis Of The Navier-Stroke Equation

824 Words4 Pages
General Equation The Navier-Strokes equation is the base of basic lubrication theory to solve the problem. The fluid characteristics such as density and viscosity are kept almost constant to solve the fluid flow problem. There are following problems which are solved by Navier-Stroke equation:- Laminar unidirectional flow between stationary parallel plates. Laminar unidirectional flow between parallel plates having relative motion. Laminar flow in circuit pipes. Laminar flow between concentric rotating cylinders. The Navier-Stroke equation can be written as following:- ρ (Du )/dt=ρX- (∂p )/∂x+ (∂ )/∂x {ɳ[ 2 (∂u )/∂x- (2 )/3 ((∂u )/∂x+(∂v )/∂y+(∂w )/∂z)]} + (∂ )/∂y [ɳ((∂u )/∂y+ (∂v )/∂x)]+ (∂ )/∂z [ɳ((∂u )/∂z+ (∂w )/∂x)]…show more content…
A typical value h/L is about 10-3. After these assumptions the Navier-Stroke equation deduced into following equations:- u ∂u/∂x+ v ∂u/∂y=(-∂P)/∂x+μ((∂^2 u)/(∂x^2 )+(∂^2 u)/(∂y^2 ) ) ………..…………………….. (5) u ∂v/∂x+ v ∂v/∂y=(-∂P)/∂y+μ((∂^2 v)/(∂x^2 )+(∂^2 v)/(∂y^2 ) ) …………………..................… (6) And continuity equation is ∂u/∂x+ ∂v/∂y=0 …………...…………………………………………… (7) W =∫_0^L▒〖∫_0^B▒〖P dx dx〗 〗 ……………….…………………………………. (8) Ff = ∫_0^L▒∫_0^B▒〖τ dx dx〗 ……………………………………………… (9) μ= W/(F_f ) …………………………………………………..……. (10) The equations 8,9 and10 are used to calculate the load caring capacity, friction force and coefficient of friction. Geometries Used and Parametric study The current work has been taken to study the different shape of geometry (cylindrical and sectors with offset and change in orientation) effects in the sliding bearing performance. The hydrodynamic plain slider bearing is shown in the figure 3.1 which having a stationary plate and a moving plate separated by the lubricant oil. The direction of motion and the inclination are given such a way that the convergent film is…show more content…
The textured parameters include height ratio and area density ratio of dimple. The performance parameters of textured surface are compared relative to the plane sliding bearing. There are following ratios which are used to study the whole problem:- Load carrying capacity ratio = (load carrying capacity of dimpled baering (W_d))/(load carrying capacity of plane baering (W)) Coefficient of friction ratio = (Coefficient of frictional force of dimpled baering (μ_d))/(Coefficient of frictional force of plane baering (μ)) Volume flow rate ratio= (Volume flow rate of dimpled baering (Q_d))/(Volume flow rate of plane baering (Q)) Height ratio(ζ) = (dimple depth of the bearing ( h_d))/( minimum film thickness of baering ( h2)) Area density (α) = (Area of the dimple (A_d ))/( Area of baering ( A) ) × 100 Attitude (λ) = (Minimum Thickness (h1))/(Maximum Thckness