Blood plasma (at 37^∘ C ) is to be supplied to a patient at the rate of 2.8 ×10^-6 m^3 / s . If

step 1 that needs to be supplied to a patient at 2 .8 times 10 to the minus 6 meters cubed per second.

Blood plasma (at 37^∘ C ) is to be supplied to a patient at...

Blood plasma (at $37^{\circ} \mathrm{C}$ ) is to be supplied to a patient at the rate of $2.8 \times 10^{-6} \mathrm{m}^{3} / \mathrm{s} .$ If the tube connecting the plasma to the patient's vein has a radius of $2.0 \mathrm{mm}$ and a length of $50 \mathrm{cm},$ what is the pressure difference between the plasma and the patient's vein?

Key Concepts

Tube Geometry

Tube geometry encompasses the dimensions of the tube, such as its radius and length, which significantly affect the resistance to flow. Particularly, the radius has a fourth-power relationship with flow resistance in the Hagen-Poiseuille equation, making even small changes in radius have a large impact on the required pressure difference for a given flow rate.

Hagen-Poiseuille Law

The Hagen-Poiseuille law describes how the volumetric flow rate of an incompressible, Newtonian fluid through a long, cylindrical tube is related to the pressure difference, the viscosity of the fluid, and the geometry of the tube. It provides a foundational equation in fluid mechanics for laminar flow in pipes and is especially useful in calculating flow parameters in biomedical and engineering applications.

Viscosity

Viscosity is a measure of a fluid's internal resistance to flow or deformation. It plays a critical role in determining how much pressure difference is required to achieve a certain flow rate, as more viscous fluids require greater pressure to overcome internal friction and maintain flow.

Laminar Flow

Laminar flow refers to a type of fluid motion where the fluid travels in parallel layers with minimal disruption between them. This organized flow regime ensures that the assumptions behind the Hagen-Poiseuille law are valid, making it possible to accurately predict flow rates and pressure differences in systems where turbulence is absent.

Pressure Difference

Pressure difference, or pressure drop, is the force that drives fluid flow through a system. In the context of tube flow, it arises from the difference in pressure between two points along the tube, overcoming viscous resistance and allowing the fluid to flow at a specified rate.

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