An insulin pump is an advanced device used for intensive insulin therapy in diabetic patients. Failure of the insulin pump sets can disrupt normal insulin delivery, leading to abnormal blood glucose elevations and potentially causing diabetic ketoacidosis, which can be life-threatening. Establishing a mathematical model to describe the fault mechanisms of insulin pump sets is fundamental for its fault diagnosis. Insulin pumps, however, provide difficulties for modeling and fault mechanism analysis due to the stiff and elastic restrictions of the needles and tubes, as well as the multi-domain interactions between the fluid (insulin) and the solid parts of the pump. In response to these challenges, this paper establishes a mathematical model of fluid transmission in insulin pumps under both healthy and faulty conditions, based on power flow theory, focusing on two typical faults: blockages and leaks. The impact of these faults on fluid flow within the insulin pump sets is quantitatively analyzed. The computational results of the proposed model showed a maximum error of 0.57% when compared with professional fluid dynamics software simulations. Furthermore, the impact of varying degrees of leakage and blockage faults on the output flow rate and pressure of the insulin pump system is analyzed. Specifically, for blockage faults, it was observed that when the blockage layer thickness is less than 0.6 mm, the changes in insulin output flow rate and the pressure within the insulin pump chamber are not significant. However, the blockage has a considerable impact on both flow rate and pressure when the thickness of the blockage layer surpasses 0.6 mm. The impact grows with the thickness of the blockage layer.