The Influence of Bends on Fluid Transients Propagated in Incompressible Pipe Flow

The influence of a bend on the fluid transients propagated by a rapid valve closure in a long pipeline is examined by means of a short dimensional analysis and a comprehensive series of experimental tests designed to record the effects of varying in turn: the pipeline diameter to thickness ratio (7.35 to 48), pipe elasticity to fluid bulk modulus ratio (0.27 to 93.6), the restraint applied to the pipeline, the bend radius of curvature to pipe bore ratio (0 to 5), the included angle of the bend (0° to 135°) and the initial flow velocity. From these tests the influence of a bend is found to be solely dependent on its geometry. Empirical formulae are proposed which express the reflection and transmission of a transient at a bend in terms of the bend radius of curvature to pipe bore ratio and included angle. The formulae are tested by varying both the angle and curvature of a series of bends mounted in turn in a steel pipeline and found to be accurate within the limits of measurement possible. A method designed to predict the effect of a multiple bend made up of a series of bends the individual reflection and transmission coefficients of which were known or predictable is tested and found to be accurate to within ±7 per cent.