**Problem Statement:**At a given instant, the blood pressure in the heart is \(1.7 \times 10^4 \, \text{Pa}\). If an artery in the brain is 0.46 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.**Discussion:**In this problem, we are asked to determine the pressure within an artery in the brain given the pressure at the heart and the vertical distance between the heart and the brain. We are to disregard any pressure changes attributable to the dynamic flow of blood, implying that we should focus on the hydrostatic pressure difference.**Key Concepts:**1. **Pascal's Principle:** When dealing with fluids at rest (hydrostatics), the pressure change in an incompressible, static fluid is given by the hydrostatic pressure equation: \[ P_2 = P_1 + \rho g h \] Where: - \( P_2 \) is the pressure at the point in question (artery in the brain). - \( P_1 \) is the initial pressure (pressure in the heart). - \( \rho \) is the density of the blood (assumed to be 1060 kg/m³). - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). - \( h \) is the height difference (0.46 m in this case).2. **Hydrostatic Pressure Calculation:** The difference in heights within a vertical column of fluid results in a difference in pressure between the top and the bottom: \[ \Delta P = \rho g h \]**Application to the Problem:**Given:- The pressure in the heart, \( P_1 = 1.7 \times 10^4 \, \text{Pa} \)- The height difference, \( h = 0.46 \, \text{m} \)- The density of blood, \( \rho = 1060 \, \text{kg/m}^3 \)- The acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)We need to find the new pressure \( P_2 \) in the artery located in the brain.First, calculate the

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Description: **Problem Statement:**At a given instant, the blood pressure in the heart is \(1.7 \times 10^4 \, \text{Pa}\). If an artery in the brain is 0.46 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.**D

Here Blood pressure in the heart = P1 = 1.7 × 104 PaWe have to calculate the blood pressure in the…

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At a given instant, the blood pressure in the heart is 1.7 x 104 Pa. If an artery in the brain is 0.46 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.

At a given instant, the blood pressure in the heart is 1.7 x 104 Pa. If an artery in the brain is 0.46 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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