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In fluid mechanics, plug flow is a simple model of the velocity profile of a fluid flowing in a pipe. In plug flow, the velocity of the fluid is assumed to be constant across any cross-section of the pipe perpendicular to the axis of the pipe. The plug flow model assumes there is no boundary layer adjacent to the inner wall of the pipe.
For a sudden expansion in a pipe, see the figure above, the Borda–Carnot equation can be derived from mass-and momentum conservation of the flow. [7] The momentum flux S (i.e. for the fluid momentum component parallel to the pipe axis) through a cross section of area A is – according to the Euler equations:
The Hazen–Williams equation is an empirical relationship that relates the flow of water in a pipe with the physical properties of the pipe and the pressure drop caused by friction. It is used in the design of water pipe systems [ 1 ] such as fire sprinkler systems , [ 2 ] water supply networks , and irrigation systems.
Once the friction factors of the pipes are obtained (or calculated from pipe friction laws such as the Darcy-Weisbach equation), we can consider how to calculate the flow rates and head losses on the network. Generally the head losses (potential differences) at each node are neglected, and a solution is sought for the steady-state flows on the ...
r = radius of the pipe (for a pipe of circular section, the internal radius of the pipe). v = mean velocity of fluid flowing through the pipe. A = cross sectional area of the pipe. In long pipes, the loss in pressure (assuming the pipe is level) is proportional to the length of pipe involved.
The laminar flow through a pipe of uniform (circular) cross-section is known as Hagen–Poiseuille flow. The equations governing the Hagen–Poiseuille flow can be derived directly from the Navier–Stokes momentum equations in 3D cylindrical coordinates ( r , θ , x ) by making the following set of assumptions:
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High velocity flows will cause some vegetation (such as grasses and forbs) to lay flat, where a lower velocity of flow through the same vegetation will not. [8] In open channels, the Darcy–Weisbach equation is valid using the hydraulic diameter as equivalent pipe diameter. It is the only best and sound method to estimate the energy loss in ...