Complete Question
If you are lying down and stand up quickly, you can get dizzy or feel faint. This is because the blood vessels don’t have time to expand to compensate for the blood pressure drop. If your brain is 0.4 m higher than your heart when you are standing, how much lower is your blood pressure at your brain than it is at your heart? The density of blood plasma is about 1025 kg/m3 and a typical maximum (systolic) pressure of the blood at the heart is 120 mm of Hg (= 0.16 atm = 16 kP = 1.6 × 104 N/m2).
Answer:
The pressure at the brain is [tex]P_b = 89.872 \ mm \ of \ Hg[/tex]
Explanation:
Generally is mathematically denoted as
[tex]P = \rho gh[/tex]
Substituting [tex]1025 kg/m^3[/tex] for [tex]\rho[/tex](the density) , [tex]9.8 m/s^2[/tex] for g (acceleration due to gravity) , 0.4m for h (the height )
We have that the pressure difference between the heart and the brain is
[tex]P = 1025 * 9.8 *0.4[/tex]
[tex]= 4018 N/m^2[/tex]
But the pressure of blood at the heart is given as
[tex]P_h=120 mm of Hg =[/tex] [tex]120 * 133 = 1.59*10^3Pa[/tex]
Now the pressure at the brain is mathematically evaluated as
[tex]P_b = P_h - P[/tex]
[tex]= 1.596*10^4 - 4018[/tex]
[tex]= 11982 N/m^2[/tex]
[tex]P_b= \frac{11982}{133} = 89.872 \ mm \ of \ Hg[/tex]
