224 VISCOSITY. [CHAP. ix. 



The total flux across any section of the pipe is 



u ZTTT dr = ?ra 4 A ^ A. 



o IS 



If now in a length I of the pipe the pressure fall from p l to j&amp;gt; 2 , we 

 have, by (20), 



and the flux is 



If /3 = co , there is no slipping at the boundary, and (22) then re 

 duces to its first term 



Poiseuille found in his experiments* on the flow of water 

 through capillary tubes that the time of efflux of a given quantity 

 of water was directly as the length of the tube, inversely as the 

 difference of pressure at the two ends, and inversely as the fourth 

 power of the diameter. These results agree with (22a). 



A comparison of the formula (22a) with experiments of this 

 kind would give the means of determining ///. 



183. Example 2. To investigate the effect of internal friction 

 on the motion of plane waves of sound. If as in Art. 166 we neg 

 lect the squares and products of small quantities, the equation of 



motion is 



du _ I dp , d?u 



di = ~pfa+ f * do* 9 



-1C. 



or, writing ^=-77, and eliminating p as before by means of the 

 dt 



relation p oc p , 



To fix the ideas let us suppose that at the plane x a simple 



vibration of period - is kept up, so that 



(24), 



* M6m. des Sav. Strangers, t. 9, 1846. Quoted by WiUlner, Experimental 

 2&amp;gt;liysik, t. 1, p. 329. 



