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PRESSURE/HEAD LOSSES IN PIPES A quantity of interest in the analysis of pipe flow is the pressure drop Δp since it is directly related to the power requirements of the fan or pump to maintain flow. The symbol Δ is typically used to indicate the difference between the final and initial values (like Δy =y 2 - y 1 ) but in fluid flow, Δp is used to designate pressure drop, and thus it is p 1 - p 2 , where p 2 is the downstream pressure and p 1 is the upstream pressure. A pressure drop due to viscous effects represents an irreversible pressure loss, and it is called pressure loss and is denoted Δp L to emphasize that it is a loss (just like the head loss h L , which is proportional to it). In practice, the pressure loss Δp L when a fluid of viscosity µ flows through a pipe of constant diameter D and length L at average velocity V can be expressed as: Δp L =λ L D ρV 2 2 (1) where the quantity λ is known as the friction factor. Equation (1) could be used to express the pressure loss for all types of fully developed internal flows (laminar or turbulent flows, circular or noncircular pipes, smooth or rough surfaces, horizontal or inclined pipes). Observation shows that in pipe flow the friction factor λ is strongly dependent on whether the flow is laminar or turbulent . In laminar flow, the friction factor is given by Eq (2) : λ = 64 Re (2) One of the interesting characteristics of laminar flow is that for the normal range of roughness encountered in pipes, neither the friction factor nor the pressure drop depends on the relative roughness. In turbulent flow the friction factor and pressure drop are functions of the relative roughness and the Reynolds number. There are no analytical solutions to turbulent flow, so in this case we must rely on the large body of empirical observations. The data were
