The 1-D axial, laminar, Newtonian flow through a tube of uniform, but noncircular, cross-section is analyzed. The tube boundary is r = R[1 + epsilon f(theta)], in which R is a reference radius, epsilon is a Small parameter and the function f(theta) of the polar angle is general, albeit subject to minimal constraints ensuring single-valuedness and quadrant symmetry. All results ave determined as asymptotic expansions complete to terms O(epsilon(2)), which include the velocity distribution, average velocity, volume flow rate, ratio of flow rates in the noncircular to that in a circular pipe of the same cross-sectional area, the friction factor-Reynolds number dependence, the permeability of packed beds comprising noncircular capillaries, kinetic-energy and momentum-flux correction factors, the capillary penetration rate under the influence of the capillary pressure and the equilibrium value of the capillary rise. Expressions are derived in terms of the general boundary function f(theta) and, for special cases, when f(theta) = sin(2k)theta (k = 1, 2, 3) and f(theta) = sin(2)k theta with k a positive integer. The results provide quantitative measures of the effect of tribe shape on flow properties and on imbibition and drainage from noncircular capillaries.