Analytical expressions are derived for the velocity field, and effective slip lengths, associated with pressure-driven longitudinal flow in a circular superhydrophobic pipe
whose boundary is patterned with a general arrangement of longitudinal no-shear stripes not necessarily possessing any rotational symmetry. First, the flow in a superhydrophobic
pipe with M different no-shear stripes in general position is found for M = 1, 2, 3. The method, which is based on use of so-called prime functions, is such that with these cases
covered, generalisation to any M ⩾ 1 follows in a straightforward manner. It is shown how any one of these solutions can be generalised to solve for flow along superhydrophobic pipes where that pattern of M menisci is repeated N ⩾ 1 times around the boundary in a rotational symmetric arrangement. The work provides an extension of the canonical pipe flow solution for an N-fold rotationally symmetric pattern of no-shear stripes due to Philip (Angew. Math. Phys., vol. 23, 1972, pp. 353–372). The novel solution method, and the solutions that it produces, have significance for a wide range of mixed boundary value problems involving Poisson’s equation arising in other applications.