(a) Determine the speed at which blood is flowing through an artery with a radius of 5.40 × 10-3 m, if the artery is supplying blood to the brain at a volume flow rate of 3.20 x 10-6 m3/s. See if you can write an expression which relates the volume flow rate of a fluid to the cross sectional area of the fluid conduit and the speed at which the fluid is traveling through the conduit. m/s (b) If the flow rate is to remain the same through a constriction that reduces the radius of the artery by a factor of 7, determine the speed at which blood must flow through the constricted region. See if you can use the equation of continuity to determine the speed at which blood is traveling through the constricted area. m/s

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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### Blood Flow Dynamics in Arteries

#### Problem Statement

(a) **Determine the speed** at which blood is flowing through an artery with a radius of \(5.40 \times 10^{-3}\) m, if the artery is supplying blood to the brain at a volume flow rate of \(3.20 \times 10^{-6}\) m\(^3\)/s.

- **Instructions**: See if you can write an expression which relates the volume flow rate of a fluid to the cross-sectional area of the fluid conduit and the speed at which the fluid is traveling through the conduit. (Units: m/s)

(b) If the flow rate is to remain the same through a **constriction** that reduces the radius of the artery by a factor of 7, **determine the speed** at which blood must flow through the constricted region.

- **Instructions**: See if you can use the equation of continuity to determine the speed at which blood is traveling through the constricted area. (Units: m/s)

---

Utilize relevant equations in fluid dynamics to solve these problems, particularly the relationship between volume flow rate, cross-sectional area, and flow velocity, as well as the equation of continuity in fluid flow.
Transcribed Image Text:### Blood Flow Dynamics in Arteries #### Problem Statement (a) **Determine the speed** at which blood is flowing through an artery with a radius of \(5.40 \times 10^{-3}\) m, if the artery is supplying blood to the brain at a volume flow rate of \(3.20 \times 10^{-6}\) m\(^3\)/s. - **Instructions**: See if you can write an expression which relates the volume flow rate of a fluid to the cross-sectional area of the fluid conduit and the speed at which the fluid is traveling through the conduit. (Units: m/s) (b) If the flow rate is to remain the same through a **constriction** that reduces the radius of the artery by a factor of 7, **determine the speed** at which blood must flow through the constricted region. - **Instructions**: See if you can use the equation of continuity to determine the speed at which blood is traveling through the constricted area. (Units: m/s) --- Utilize relevant equations in fluid dynamics to solve these problems, particularly the relationship between volume flow rate, cross-sectional area, and flow velocity, as well as the equation of continuity in fluid flow.
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