Mechanical shaft seals for pumps - Grundfos

z
F
V = V 0
V = 0
Thus, the shear stress F/A is proportional to the change of shear strain, v 0 /h:
F/A = h v 0 /h
∂
∂x(h 3 (x) ) + (h = 6v . η
3 (x) )
∂p ∂ ∂p
∂h(x)
Or more generally with t as shear stress:
∂x ∂y ∂y
∂x
Area A
h
Area A
In the case of parallel faces shown in fig. 4.3, the velocity distribution does not cause any pressure
increase. If one of the surfaces is tilted slightly, the fluid will be forced into a smaller cross-
V = V
section and therefore compressed. This 0
F will cause the pressure to increase and V create a
N
0
pressure F distribution between the surfaces. See fig. 4.4.
y
z
h 1
F
x
h(x)
V = V 0
Fig. 4.3: Velocity distribution and shear resistance, F, of a fluid film between two surfaces,
h being the distance between V = the 0 surfaces
y
F N
h 1
x
∂ t = h ∂v/∂h (Newtonian fluids)
∂x(h 3 ∂p ∂
(x) ) + = 6v . η
∂x ∂y (h3 ∂p
(x)
∂y)
h(x)
V = 0
p (x, y)
p (x, y)
Fig. 4.4: Slightly tilted moving surface creating a pressure profile
∂h(x)
∂x
For a given geometry, the pressure profile can be calculated using the Reynolds equation:
The lubricating film calculated depends on velocity, v 0 , and load, F N . However, in all cases the
pressure distribution generated between the surfaces will only be able to separate the surfaces
by a distance comparable to the wedge height (h 2 – h 1 ). See fig. 4.4.
More details about lubrication theory can be found in [2].
F N
∂
∂x(h 3 ∂p ∂
(x) ) + = 6v . η
∂x ∂y (h3 ∂p
(x)
∂y)
∂h(x)
∂x
h 2
h 2
V 0
h
Area A
V 0
h
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