This paper discusses the motion of fluid in a curved pipe, focusing on the secondary motion that occurs in the plane of the cross-section. In addition to the primary motion along the pipe, a secondary motion is present, which reduces the rate of flow for a given pressure gradient and causes the region of maximum primary motion to shift outward. These effects are difficult to deduce from the exact equations of motion, but can be understood by assuming the secondary motion is replaced by a uniform stream. The appropriate velocity of this stream can be determined from experimental relations between flow rate and pressure gradient. The equations of motion and continuity are derived for fluid flow in a curved pipe, assuming the velocity components are independent of the angular coordinate and time. These equations are simplified by replacing certain operators and terms, leading to approximate equations that describe the flow. The pressure is found to have a specific form, and the velocity components are expressed in terms of a stream function. The equations are then non-dimensionalized, allowing for the analysis of flow in both circular and rectangular cross-sections. For a circular cross-section, the solution involves Bessel functions, and the flow rate is found to decrease with increasing curvature. For a rectangular cross-section, the solution involves hyperbolic functions, and the flow rate is also found to decrease with increasing curvature. The results show that the secondary motion reduces the flow rate, and the region of maximum velocity shifts outward, explaining the cutting of a curved stream into the outer bank. Experimental results confirm the theoretical predictions, showing that the ratio of secondary to primary flow reaches a maximum. The paper concludes that the secondary motion significantly affects the flow in curved pipes, and the results provide a basis for understanding and predicting flow behavior in such systems.This paper discusses the motion of fluid in a curved pipe, focusing on the secondary motion that occurs in the plane of the cross-section. In addition to the primary motion along the pipe, a secondary motion is present, which reduces the rate of flow for a given pressure gradient and causes the region of maximum primary motion to shift outward. These effects are difficult to deduce from the exact equations of motion, but can be understood by assuming the secondary motion is replaced by a uniform stream. The appropriate velocity of this stream can be determined from experimental relations between flow rate and pressure gradient. The equations of motion and continuity are derived for fluid flow in a curved pipe, assuming the velocity components are independent of the angular coordinate and time. These equations are simplified by replacing certain operators and terms, leading to approximate equations that describe the flow. The pressure is found to have a specific form, and the velocity components are expressed in terms of a stream function. The equations are then non-dimensionalized, allowing for the analysis of flow in both circular and rectangular cross-sections. For a circular cross-section, the solution involves Bessel functions, and the flow rate is found to decrease with increasing curvature. For a rectangular cross-section, the solution involves hyperbolic functions, and the flow rate is also found to decrease with increasing curvature. The results show that the secondary motion reduces the flow rate, and the region of maximum velocity shifts outward, explaining the cutting of a curved stream into the outer bank. Experimental results confirm the theoretical predictions, showing that the ratio of secondary to primary flow reaches a maximum. The paper concludes that the secondary motion significantly affects the flow in curved pipes, and the results provide a basis for understanding and predicting flow behavior in such systems.