16 



TWO FLUIDS IN A BENT TUBE. 



multiplying (2) by w, and subtracting the result from (1), 



\\v have 



(w 1 w)cP = (w' - ^v) dQ, 



.-. cP = dQ, 

 and hence BC is horizontal. 



That is, the common surface of two fluids that do 

 not mix is a horizontal plane. 



COR. This proposition is- true, whatever be the number 

 of fluids ; the common surfaces are all horizontal. If, 

 therefore, the number he infinite, or the density of the fluid 

 vary according to any law, the surface of each will still be 

 horizontal.* 



13. Two Fluids in a Bent Tube Let A and C be 



the two surfaces, B the common surface, 

 and p, p' the densities of AR and BC. 

 Let z and z' represent the heights of 

 the surfaces A and C, above the com- 

 mon surface B, and take B' in the 

 denser fluid in the same horizontal 

 plane as B. 

 Then we have, Fig. a 



the pressure at B = gpz [(7) of Art. 10] ; 

 the pressure at B' = gp'z', 

 and these are equal (Art. 11, Cor. 3). 



B- 



B' 



z: z 



p : p. 



Hence, when two fluids that do not mix together 

 meet in a bent tube, the heights of their upper sur- 



See Beuam's Hydrostatics, p. 31 ; also Eland's Hydrostatics, p. 20. 



