What is the difference in blood pressure (mm-hg) between the bottom of the feet and the top of the head of a 1.87-m-tall person standing vertically? 1 mm-hg = 133 n/m2. the density of blood is 1050 kg/m3?

Respuesta :

Using the hydraulic principle, hydraulic pressure is uniform in all directions of a static liquid, and increases with depth according to density.


Assuming the variation of blood pressure is the same as a static liquid, we need to find the difference according to height.

A column of 1.87 m of blood exerts a pressure of

1.87*1050 kg/m^3*9.81

= 19261 n/m^2 or 19261 Pa


Convert to mm-Hg

= 19261 n/m^2/ 133 (n/m^2/mm-Hg)

= 144.8 mm-Hg

= 145 mm-Hg (to three significant figures)

The difference in blood pressure (mm-hg) between the bottom of the feet and the top of the head is 145 mm-Hg.

What is the basic principle of hydraulics?

The basis for all hydraulic systems is expressed by Pascal's law which states that the pressure exerted anywhere upon an enclosed liquid is transmitted undiminished, in all directions, to the interior of the container.

This principle allows large forces to be generated with relatively little effort.

Using the hydraulic principle,

Hydraulic pressure is uniform in all directions of a static liquid, and increases with depth according to density.

From the given question,

The variation of blood pressure is the same as a static liquid,

So we find the difference according to height.

A column of 1.87 m of blood exerts a pressure of

= 1.87 x 1050 kg/m³ x 9.81

= 19261 n/m² or 19261 Pa

Let convert it to mm-Hg

=[tex]\frac{ 19261 n/m^2}{133 (n/m^2/mm-Hg)}[/tex]

= 144.8 mm-Hg

= 145 mm-Hg (Approx.)

Therefore ,

145 mm-Hg is  the difference in blood pressure (mm-hg) between the bottom of the feet and the top of the head.

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