To ensure a reasonable and cost-effective design pressure for the new composite polyurethane (PU) oil transfer hose, this study presents a mathematical model and hydraulic friction calculation formulas that account for variations in hydraulic friction resulting from the decrease in the elastic modulus. The hydraulic grade line of the PU hose exhibits a nonlinear equation with continuous curvature changes. To address this, we investigate a specific mathematical description method and employ numerical calculation methods to computerize the graphical calculation process. Additionally, the study examines the new pressure energy balance relationship in various transportation scenarios, such as fluctuating flow rates and cross-station transport, laying the groundwork for optimizing the operation plan.