184 Dr Searle, A Simple Method of determining 
direction from A to B. Let CD be a length dz of a coaxal 
geometrical cylinder of radius r cm., the end C being at a distance 
x cm. from the end A of the tube. 
Let the velocity of the air in the positive direction at any 
point defined by 7 and x be v cm. per sec. Then the velocity 
gradient at the curved surface of the cylinder CD is dv/dr sec, 
Hence, if the viscosity of the air be 7 dynes per sq. cm. per unit 
velocity gradient or 7 grm. cm.~ sec.—, the force due to viscous | 
action on the curved surface of CD in the positive direction is 
du 
Serer 2nrda dynes. 
If the pressure at any point on the end C of the cylinder be | 
p dynes per sq. cm., the pressure at any point on the end D is 
p +(dp/da) dx, and thus the resultant in the positive direction of 
the forces due to the pressures is 
2p 
eat oa dx dynes. 
When the velocity of the air at any point in the tube is very | 
small compared with the velocity of sound in air, the rate at which 
momentum enters the cylinder CD by the end C by convection 
differs from the rate at which it leaves the cylinder by the end D 
by an amount negligible compared with zr? (dp/dx) da. Since the 
motion is steady, the momentum within the cylinder remains 
unchanged. Hence the resultant force vanishes and thus 
st Ge 
1G, aarda — ar do 0 = 9 
dvr dp 
dr 2 dx’ CO ay (i) 
Since v =0 when r=<a, because there is no slipping at the wall of 
the tube, the solution of this equation is 
or 
1 
fy BY = ‘ 9 
v=—— (a Dae 230) Gee ae (2) 
If the flow of air across the plane defined by « be U cc. per sec., 
U= ["2nrodr=— 5 e [@=r)rar 
ae 8 ae” ele svele!aiaje is)e/u''s eiuin aisles /eleleleanieledstateletuielakeietene tenons (3) 
The mass of air crossing this plane per second is oU grammes, 
where o grm. per cc. is the density of the air under the pressure p 
at the temperature @ prevailing at the plane «; this temperature 
