This paper models and analyzes flows in linear and curved microchannels on a rotating Laboratory Compact Disk (LabCD). The effects of centrifugal force are introduced into the governing equations of the microchannel flow to promote the fluidic velocity in the microchannel. The microchannel types on the LabCD must be designed following a process of mathematical identification. A flow model which takes into account the combined effects of viscosity, capillary forces, pressure difference and rotation is developed. A reduction-order technique is applied to obtain linear and nonlinear governing equations for flows in straight and curviform microchannels, respectively. The analytical solutions for the flow in the tubular microchannel are obtained using the Laplace transform method, while the numerical solutions for the curviform microchannel or microchannel with a varying cross-section are obtained using a piecewise linear method. The results show that the analyzed models are easily presented by a mathematical expression for the case of a tubular microchannel and simulated using a numerical program for the case of special microchannels. The modeling presented in this paper enables the performance of LabCD devices to be significantly enhanced by providing insights into the fluid flow behavior in microchannels of varying configurations under different rotational velocities.