THE UNSTEADY MOTION OF VISCOUS LIQUIDS IN 
CAPILLARY TUBES. 
HENRY CHARLES WOLFF. 
When a clean glass tube is dipped into water, the liquid will 
rise in it to a certain height, where it will come to rest with a 
concave surface. The amount of the liqu which is raised above 
the general level depends, as is well known jpon the angle of con¬ 
tact of this surface, or meniscus, with the walls of the tube, and 
also upon the strength of the surface film. The exact form of the 
meniscus when the liquid is in motion is unknown. Not only 
is its form different from that which it assumes while at rest, 
but its shape probably varies with different velocities of the 
liquid. Under these conditions it seems likely that the pull 
due to surface tension varies with different velocities of the 
liquid as it ascends a vertical or flows along a horizontal tube. 
In the following work I shall attempt to obtain an expression 
for the velocity of the meniscus along a horizontal tube, sup¬ 
posing that the liquid is forced into one end of the tube under 
a constant head. 
When a liquid is allowed to flow from one reservoir into an¬ 
other through a horizontal capillary tube, we know that the 
discharge per unit of time, Q, is given by the equation, 
q = x- 
7t a 4 p 
M pl’ 
( 1 ) 
in which a is the radius of the tube, l is its length, ^ is the co¬ 
efficient of viscosity, p is the density of the liquid, and p is the 
difference between the pressures at the two ends of the tube. 
From this we obtain for the velocity, 
a 2 p 
M pl' 
(2) 
