Postural hypotension is the occurrence of low (systolic) blood pressure when sta

Question

Postural hypotension is the occurrence of low (systolic) blood pressure when standing up too quickly from a reclined position, causing fainting or lightheadedness. For most people, a systolic pressure less than 90 mm of Hg is considered low.

If the blood pressure in your brain is 120 mm when you are lying down, what would it be when you stand up? Assume that your brain is 40 cm from your heart and that = 1060 kg/m3 for your blood. Note: Normally, your blood vessels constrict and expand to keep your brain blood pressure stable when you change your posture.

Explanation / Answer

Use Bernouilli's law in the form

delta(p) = -rho g delta(h)
= -1060 kg/m^3 * 9.81 m/s^2 * 0.40m
= -4159.44 N/m^2

We know that 760 mmHg corresponds to 1.013*10^5 N/m^2.

So this is

delta(p) = -4159.44/(1.013*10^5)*760 mmHg
= -31.21 mmHg   

120mmHg - 31.2mmHg = 88.8 mmHg

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