FLUIDS AND THE DETERMINATION OF THE CRITERION. 151 
Case I. Conditions. 
26. The fluid is of constant density p and viscosity m, and is caused to flow, by 
a uniform variation of pressure dp/dx, in direction x between parallel surfaces, 
given by 
Yi Freeh Oye Y= hO gee My Wel eh oie “ates es, (28) 
the surfaces being of indefinite extent in directions z and @. 
The Boundary Conditions. 
(1.) There can be no motion normal to the solid surfaces, therefore 
O—=5 0 whten yi —s sje Oni ewe) eee ens ace (29) 
(2.) That there shall be no tangential motion at the surface, therefore 
C—O OW when Se0) 5 8 5 6 eon 5 (80))S 
whence by equation (21), putting w for u’, py, = — pdu/dy. 
By the equation of continuity du/dx + dv/dy + dw/dz = 0, therefore at the 
boundaries we have the further conditions, that when y = + by, 
Siti City = CCB O 5 6 6 2 os o (Sil), 
Singular Solution. 
27. If the mean-motion is everywhere in direction , then, by the equation of 
continuity, it is constant in this direction, and as shown (Art. 8) the periods of mean- 
motion are infinite, and the equations (1), (3), and (9) are strictly true. Hence if 
| 
DS ties OL! 8h oe eas See me eee ey (oP) 
we have conditions under which a singular solution of the equations, applied to this 
case, is possible whatsoever may be the value of b,, dp/dz, p and yp. 
Substituting for p,,, p,:, &¢., in equations (1) from equations (21), and substituting 
uv for u’, &c., these become 
du dp du du 
pan tele tas) HOOKS NESE: Pome) 
