Question

The maximum blood pressure in the upper arm of a healthy person is about 120 mmHg. Determine how high the blood will rise in the tube if a vertical tube open to the atmosphere is connected to the vein in the arm of the person. Take the density of the blood to be 1050 kg/m3 .

Answer 1

Answer:

1.553 m

Explanation:

This is a pressure problem.

On one side we have got the pressure from the arm's blood and on the other side we have got the pressure from blood height

$P1=P2\\P1=Patm+Parm'sblood\\P2= Patm+Pbloodheight\\Patm+Parm'sblood=Patm+Pbloodheight$

Patm is atmospheric pressure.Patm is applied on each side of the equation

Then :

$Parm'sblood=Pbloodheight$

Pbloodheight =ρ.g.h

where ρ is the blood density, g is the gravity and h is the blood height.

ρ= 1050 kg/m3

$g=9.81\frac{m}{s^{2} }$

$Parm'sblood= 120 mmHg$

$1 mmHg=133.322 Pa$

$120 mmHg.\frac{133.322Pa}{1mmHg} =15998.64 Pa\\Pa=\frac{N}{m^{2} } \\N=kg.\frac{m}{s^{2} }$

$Parm'sblood=Pbloodheight\\15998.64 Pa=1050\frac{kg}{m^{3} } .9.81\frac{m}{s^{2} } .h\\\\h=\frac{15998.64 Pa}{1050\frac{kg}{m^{3} } .9.81\frac{m}{s^{2} } } \\h=1.553m$