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Pressure drop (often abbreviated as "dP" or "ΔP") [1] is defined as the difference in total pressure between two points of a fluid carrying network. A pressure drop occurs when frictional forces, caused by the resistance to flow, act on a fluid as it flows through a conduit (such as a channel, pipe, or tube).
In non ideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section.
Pressure has dimensions of energy per unit volume, therefore the pressure drop between two points must be proportional to the dynamic pressure q. We also know that pressure must be proportional to the length of the pipe between the two points L as the pressure drop per unit length is a constant.
The equation was derived by Kozeny (1927) [1] and Carman (1937, 1956) [2] [3] [4] from a starting point of (a) modelling fluid flow in a packed bed as laminar fluid flow in a collection of curving passages/tubes crossing the packed bed and (b) Poiseuille's law describing laminar fluid flow in straight, circular section pipes.
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.
[1] [2] [3] A key question is the uniformity of the flow distribution and pressure drop. Fig. 1. Manifold arrangement for flow distribution. Traditionally, most of theoretical models are based on Bernoulli equation after taking the frictional losses into account using a control volume (Fig. 2).
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To calculate the pressure drop in a given reactor, the following equation may be deduced: = + | |. This arrangement of the Ergun equation makes clear its close relationship to the simpler Kozeny-Carman equation, which describes laminar flow of fluids across packed beds via the first term on the right hand side.