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The Hagen–Poiseuille equation can be derived from the Navier–Stokes equations. 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 ...
In fluid dynamics, the Hagen–Poiseuille equation is a physical law that gives the pressure drop in a fluid flowing through a long cylindrical pipe. The assumptions of the equation are that the flow is laminar viscous and incompressible and the flow is through a constant circular cross-section that is substantially longer than its diameter.
The poise (symbol P; / p ɔɪ z, p w ɑː z /) is the unit of dynamic viscosity (absolute viscosity) in the centimetre–gram–second system of units (CGS). [1] It is named after Jean Léonard Marie Poiseuille (see Hagen–Poiseuille equation).
Vascular resistance is the resistance that must be overcome for blood to flow through the circulatory system.The resistance offered by the systemic circulation is known as the systemic vascular resistance or may sometimes be called by another term total peripheral resistance, while the resistance caused by the pulmonary circulation is known as the pulmonary vascular resistance.
Friction loss under conditions of laminar flow follow the Hagen–Poiseuille equation, which is an exact solution to the Navier-Stokes equations. For a circular pipe with a fluid of density ρ and viscosity μ , the hydraulic slope S can be expressed
The equation is named after Henry Darcy and Julius Weisbach. Currently, there is no formula more accurate or universally applicable than the Darcy-Weisbach supplemented by the Moody diagram or Colebrook equation. [1] The Darcy–Weisbach equation contains a dimensionless friction factor, known as the Darcy friction factor. This is also ...
This equation for the velocity is the same as that of any object falling height h C. This equation assumes P C is atmospheric pressure. If the end of the siphon is below the surface, the height to the end of the siphon cannot be used; rather the height difference between the reservoirs should be used.
Hagen–Poiseuille equation Gotthilf Heinrich Ludwig Hagen (3 March 1797 – 3 February 1884) was a German civil engineer who made important contributions to fluid dynamics , hydraulic engineering and probability theory.