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Q.40

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 385

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Short Answer

Postural hypotension is the occurrence of low systolic blood pressure when a person stands up too quickly from a reclining position. A brain blood pressure lower than of can cause fainting or lightheadedness. In a healthy adult, the automatic constriction and expansion of blood vessels keep the brain blood pressure constant while posture is changing, but disease or aging can weaken this response. If the blood pressure in your brain is of while lying down, what would it be when you stand up if this automatic response failed? Assume your brain is from your heart and the density of blood is .

At this blood pressure will cause faintness.

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Step by Step Solution

Step 1 : Introduction

The change in blood pressure as a person stands up can be modeled as the change in fluid pressure at different heights. Hence, it is fit to use the Bernoulli equation.

Step 2: Explanation

The mathematical form of Bernoulli's equation is as follows

Since the speed of the blood is considered as uniform, the above equation can be written as follows.

The variables in the above equation are described as follows.

: Blood pressure lying down, given as

: Blood pressure standing up, unknown

: Height lying down

: Height standing up

: Density of blood

: Acceleration due to gravity,

Step 3: Substitution

Isolate for from above equation.

Substitute for density of blood, for , for and for which is the distance between the heart and the brain, the same amount of displacement blood makes between heart and brain when person stands up

This blood pressure ,at , will cause nausea.

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