please help me! :(

Question

What is the difference in blood pressure (in mm of Hg) between the top of the head and bottom of the feet of a 1.61m-tall person standing vertically?  (The density of blood is approximately 1060 kg/m³)

Answer 1

To find the pressure difference we can use the hydrostatic pressure equation, which gives the pressure at a given depth for a fluid:

P = ρ x g x h, where:

P is the hydrostatic pressure,

ρ (rho) is the density of the fluid,

g is the acceleration due to gravity, and

h is the fluid depth

Between the top of the head and bottom of the feet (a distance of delta_h), the pressure difference is:

delta_P = ρ x g x delta_h

We know the values of the 3 quantities on the right hand side of this equation:

ρ = 1060 kg/m³

g = 9.8 m/sec², and

delta_h = 1.61 m

The pressure difference is then:

delta_P = (1060 kg/m³)(9.8 m/sec²)(1.61 m) = 16724.68 kg/(m sec²)

The units of the right hand side are also units of N/m², also known as units of Pascals.

To convert to mm of Hg, use:

1 kg/(m sec²) = 0.0075001 mm of Hg

... so:

delta_P = 16724.68 kg/(m sec²) * 0.0075001 mm of Hg/(kg/(m sec²)) = 125.4 mm of Hg