laminar flow in annular conduits

the flow of fluids in annular conduits has been studied for over sixty years, however the resulted data are very scattered. in this paper the problem is analytically solved, starting out with navier-stokes equations. a computer solution is used to determine the shape of velocity profiles, the discharge and the friction factor in a large number of concentric and eccentric annular conduits. the effect of eccentricity on discharge is also determined for a large range in eccentricity and b/a ratio, where a and b are the inner and outer cylinder radii. the results indicate that for ratios of b/a up to about 1. 25 the velocity profile is symmetrical. however with increase in b/a ratio as well as in eccenricity the location of maximum velocity moves closer to the inner cylinder and thus the profile is skewed. for a given ratio of b/a, the discharge is proportional to the fourth power of a or b and thus by doubling the size the discharge will be increased by a factor of 16. a relation between the dimensionless discharge aqo and ar is obtained for concentric case. for large values of ar (ar 10) the following formula: aqo=.566 ar4.07 is suggested to represent this relation.