Rapid global development has resulted in the widespread use of water pipelines in industrial and agricultural production and life. During water transportation and deployment, water pipes with different angles need to be positioned according to different geographical and topographical problems. Flowmaster simulation software was used to simulate the leakage process of pipelines with different angles. The transient characteristics of fluids in the pipeline were studied in detail. The influences of parameters, such as the bending coefficient R/D (R is the turning radius of pipe, D is the inner diameter of pipe), leakage position, and leakage aperture on the transient flow law of pipelines with and without leakage, were analyzed. The results show that the periodic decay of the upstream flow and pressure curve at the valve with and without leakage has an insignificant relationship with the bending coefficient R/D; however, the amplitude of the sudden position change is positively correlated with the magnitude of R/D. The leakage aperture is positively correlated with the leakage flow and negatively correlated with the pressure value at the leak location node. The farther the leak position is from the valve, the greater the amplitude of the valve end pressure and the upstream flow curve, and symmetric fluctuations occur.