Answer Happy

Q5: (20 marks) Pipe leakage has become a critical issue for urban water supply systems in terms of water and energy resources as well as public living quality and safety. Transient waves, which are triggered by highly unsteady pressure head variations in the pipeline, have been recently developed for an effective technology to solve pipe leakage issues, as sketched in Figure Q5 below. From the extensive uses of this innovative method, it has been found that its validity and accuracy is highly dependent on the leak-induced wave reflection measurement, which is commonly defined as reflection coefficient (Cref) as follow: Cher = hres hin where hin and href are incident and reflected waves i.e., pressure heads) measured in the system. Through theoretical analysis and experimental applications, it is evidenced that the reflection coefficient (Cref) is related to various system and fluid properties in the water supply pipelines, including: i. internal fluid properties: density (p) and kinematic viscosity (v); ii. pipeline properties: length (L), diameter (D), thickness (e), dimensionless friction factor (3), speed of sound (C), pipe deformation time (T) and creep compliance (I); iii. initial flow conditions: flow velocity (Vo) and pressure head (Ho); iv. leakage information: dimensionless size (a), and distance from measurement (d); v. transient wave generation: transient pressure head (AH), and wave frequency (w). Applying the dimensional analysis, to generate a dimensionless relationship for Cref as a function of all other given parameters above. (hint: common units of J and o are: Pal and s', respectively) Reflected Wave Flow Direction Transmitted Wave Wave Generator & measurement Incident Wave 프 2101 Leak 요 Users Water Source Pump Station Pipeline Valve Figure 25