A simple analytic geometry method is proposed in the paper to solve the force balance equation on the liquid meniscus. Based on a proper model for the macroscopic dynamic contact angle, evolution of the liquid meniscus including the moving speed and the shape is obtained. Wall condition of zero dynamic contact angle is allowed. The resulting slipping velocity at the contact line resolves the stress singularity issue successfully. Performance of the present method is examined through five well-documented capillary rise examples. Good agreements between the predictions and the measurements are observable as long as a reliable model for the dynamic contact angle is available. Although only capillary rise problem is demonstrated in this paper, concept of this method is applicable to free surface flow in the vicinity of a contact line where the capillary force dominates the flow.
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