PROFESSOR O, REYNOLDS ON THE THEORY OF LUBRICATION 
For boundary conditions 
y= 0 = iv = 0 
y=h w = U 1 iv— 0 
f{xy) = 0 p=p 0 
v— 0 ~1 
! -=Yf;+Y j. 
J 
(15) 
21. Equations (13) may now be integrated, the constants being determined by the 
conditions (15). 
The second of these equations gives p independent of y, so that the first and third 
are directly integrable, whence 
1 dp t 7 \ , tt Ji ~y i tt y "'I 
w =^X^“%+ u o-y-+U ij ' 
2fi dp 
u '=b/t ( y~ h ^ 
y h 
V 
■ (16) 
Differentiating these equations with respect to x and z respectively, and substituting 
in the last of equations (13) 
I tt y 
(f4 ° h +Ul A 
Integrating from y — 0 to y = h, and substituting from conditions (15) 
I( &3 I)+K A3 I)= 6 4 ( tj »+ u ^+ 2 y} . . . 
(U) 
From equations (16) and (14) 
w=tl(%-A)+nu 1 -u 0 )d 
2 d,v 
P * s = 2 d . 
^(2 y-A) 
J 
(181 
Putting jd for the shearing stresses at the solid on the surfaces in the directions 
x and z respectively, then taking the positive sign when y=h, and the negative 
when y —0 
^ /TT TT \ 1 —r~ 1 7 ^ 
