Solutions to Two Problems of Pipe Flow

This paper assesses two aspects of liquid flow in pipes. The first aspect is the relation between pipe critical flow depth and flow discharge. The critical flow depth in a pipe is generally expressed as an implicit function. The paper proposes two simple expressions that can be used to explicitly express pipe critical flow depth as a function of pipe diameter and discharge. The approximation errors associated with these proposed expressions were found to be within 1.0%. The second aspect is the flow transition from open pipe flow to full pipe flow in a long pipe. Theoretically, when a pipe is close to flowing full, a given discharge may correspond to multiple head differences. This paper presents a practical solution approach that yields a unique solution for the pipe flow depth for a given discharge in the transition zone.