Unsteady Flow 2.pdf

CIVL 2310 Fluid Mechanics Lecture 24: Unsteady flow in pipelines (2) 11.5.2. of “Mechanics of Fluids, ” Potter and Wiggert, Brooks/Cole, 2002. 1. Compressible flow in elastic pipe: water hammer Sudden closure of valves in pipe systems generates a pressure wave that initially travels upstream. The pressure compresses the liquid and generates small deformations on the pipe material. The incompressible flow in inelastic pipe assumptions could not be used in this case. Since the pressure wave travels at a constant velocity a, we can transform our unsteady problem by adopting a reference frame moving with the wave (Figure 1)

Figure 1 - Pressure wave moving through a segment of horizontal pipe: (a) pressure wave moving to the left at speed a; (b) pressure wave appears stationary using the principle of superposition; (c) pressure forces acting on the control volume.

Calculation of a: Combining 11.5.10 and 11.5.12 to eliminate V:

Figure 11.10 – One cycle of wave motion in a pipe due to a sudden valve closure. (after Rust, 1979)

Figure 11.11 – Pressure waveforms at the valve (p2), pipe midpoint (p4), and velocity waveform at the entrance to the pipe (V1).

Figure 11.12 – Pressure waveform at the valve for an actual pipe system following rapid valve closure. (After Martin, 1983)