What does the pressure loss of flowing fluid due to friction vary approximately with?

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The pressure loss of flowing fluid due to friction is primarily influenced by the square of the velocity. This relationship is rooted in the principles of fluid dynamics, particularly in the context of laminar and turbulent flow. When fluid flows through a pipe, the friction between the fluid and the pipe walls causes a loss of pressure, and this loss increases with the increase in the velocity of the fluid. More specifically, when the flow velocity doubles, the frictional pressure loss increases by a factor of four, demonstrating the quadratic relationship.

Additionally, this concept aligns with the Darcy-Weisbach equation, which quantifies pressure losses in pipes and includes velocity squared in its formulation. This foundational understanding is crucial for plumbing design, as it helps engineers predict and manage pressure loss within systems effectively. The implications of this relationship affect pipe sizing, material selection, and overall system efficiency in plumbing design.

Other influences, such as the mass of the fluid, diameter of the pipe, and temperature of the fluid, do play roles in determining overall pressure drop characteristics but do not have the same direct quadratic relationship with frictional pressure loss as the fluid's velocity. Understanding this relationship is vital for optimal design and operation of plumbing systems.

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