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Swimming micro robots are becoming feasible in biomedical applications such as targeted drug delivery, opening clogged arteries and diagnosis owing to recent developments in micro and nano manufacturing technologies. It has been demonstrated at various scales that micro helices with magnetic coating or attached to a magnet can move in fluids with the application of external rotating magnetic fields. The motion of micro swimmers interacting with flow inside channels needs to be well understood especially for medical applications where the motion of micro robots inside arteries and conduits in the body become pertinent. In this work, swimming of helical micro robots with magnetic heads inside tubes is modeled with the resistive force theory (RFT) and validated with experiments conducted in glycerin filled mini glass channels placed in rotational magnetic fields. The time-averaged forward velocities of magnetically driven micro swimmers that are calculated by the RFT model agree very well with experimental results.