Entry flow in a curved pipe

This paper deals with the development of the flow in a curved tube near the inlet. The solution is obtained by the method of matched asymptotic expansions. Two inlet conditions are considered: (i) the condition of constant dynamic pressure at the entrance, which may be of practical interest in applications to blood flow in the aorta; and (ii) a uniform entry condition. It is shown that the geometry and the nature of the entry condition appreciably influence the initial development of the flow. The effect of the secondary flow due to the curvature on the wall shear is discussed and it is shown that the cross-over between shear maxima on the inside and the outside of the tube occurs at a downstream distance which is 1·9 times the radius of the tube for entry condition (i) while in the case of entry condition (ii) it is 0·95 times the radius, which is half the distance required in case (i). It is found that the pressure distribution is not significantly influenced by the secondary flow during the initial development of the motion. The analysis, which is developed for steady motion, can be extended to pulsatile flows, which are of greater physiological interest.