Poiseuille`s Law for Resistance

Poiseuille`s law is widely applied in the medical field: understanding blood pressure, determining the flow of intravenous fluids, predicting vascular resistance, etc. Poiseuille`s law helps determine the viscosity of liquids used in DNA testing, chemical analysis, and fuel testing. Some other applications of Poiseuille`s law are: There are three main factors that determine resistance to blood flow in a single vessel: the diameter (or radius) of the vessels, the length of the vessels and the viscosity of the blood. Of these three factors, the diameter of the vessel is quantitatively and physiologically the most important. The reason for this is that the diameter of the vessel changes due to the contraction and relaxation of vascular smooth muscles in the blood vessel wall. In addition, very small changes in the diameter of the container, as described below, result in significant changes in strength. The length of the vessels does not change significantly, and the viscosity of the blood usually remains within a small range (except when the hematocrit changes). This is exactly Ohm`s law, where the resistance R = V/I by the formula In the body, however, the flow does not exactly match this relationship, because this relationship requires long straight tubes (blood vessels), a Newtonian liquid (e.g. water, not blood, which is not Newtonian) and conditions of continuous laminar flow. Nevertheless, the relationship clearly shows the dominant influence of the vascular radius on strength and flow and therefore serves as an important concept for understanding how physiological (e.g., vascular tone) and pathological (e.g., vascular stenosis) changes in the vascular radius affect pressure and flow, and how changes in the size of the heart valve opening (e.g., in valve stenosis) affect flow and pressure gradients through the heart valves. It follows that the resistance R is proportional to the length L of the resistance, which is true. However, it also follows that the resistance R is inversely proportional to the fourth power of the radius r, that is, the resistance R is inversely proportional to the second power of the section S = πr2 of the resistance, which differs from the electric formula. The electrical relationship for resistance is We can use [latex]boldsymbol{P_2-P_1=RQ}[/latex] to analyze pressure drops that occur in more complex systems where the radius of the pipe is not the same everywhere.

Resistance will be much greater in narrow places such as a blocked coronary artery. At a given flow rate[latex]boldsymbol{Q},[/latex], the pressure drop is greatest where the pipe is narrowest. This is how the taps control the flow. In addition, [latex]boldsymbol{R}[/latex] is significantly increased by turbulence, and shrinkage that creates turbulence significantly reduces downstream pressure. Plaque in an artery reduces pressure and therefore flow, both by its strength and the turbulence it creates. Fig. 19: An oil bubble throws crude oil 25.0 m through a pipe with a diameter of 0.100 m into the air. Taking into account the air resistance, but not the resistance of the pipe and assuming laminar flow, the overpressure at the inlet of the 50.0 m long vertical pipe is calculated. Consider the density of the oil as [latex]boldsymbol{900textbf{ kg/m}^3}[/latex] and its viscosity as [latex]boldsymbol{1.00(textbf{N/m}^2)cdotptextbf{s}}[/latex](or[latex]boldsymbol{1.00textbf{ Pa}cdotptextbf{s}}[/latex]). Note that you need to take into account the pressure due to the 50.0 m long oil column in the pipe. This equation is called Poiseuille`s law for resistance, after the French scientist J.

L. Poiseuille (1799-1869), who derived it to understand blood flow, an often turbulent fluid. The application of Poiseuille`s law of resistance is more appropriate for uniform liquids or Newtonian fluids with comparatively less turbulence. With CFD simulations, flow, flow resistance, dependence on pipe dimensions and viscosity can be easily determined. Similarly, the resistance experienced by the flow of the fluid is also different. Fluid flow resistance can be defined as the ratio of pressure difference to flow. From the expression of Poiseuille`s law, the flow resistance can be deduced as follows: The Hagen-Poiseuille equation is useful for determining the vascular resistance and thus the flow rate of intravenous (IV) fluids, which can be obtained with different sizes of peripheral and central cannulas. The equation indicates that the flow rate is proportional to the radius of the fourth power, which means that a slight increase in the inside diameter of the cannula results in a significant increase in the flow of fluids IV. The radius of IV cannulas is usually measured in “gauge”, which is inversely proportional to the radius.

Peripheral IV cannulas are usually available in 14G, 16G, 18G, 20G, 22G, 26G (large to small). For example, the flow of a 14G cannula is usually about twice that of a 16G cannula and ten times that of a 20G cannula.

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