Giraffe bending to drink. In a giraffe with its head 1.83 m above its heart, and its heart 2.04 m above its feet, the (hydrostatic) gauge pressure in the blood at its heart is 246 torr. Assume that the giraffe stands upright and the blood density is 1.06 * 103 kg/m3. In torr (or mm Hg), find the (gauge) blood pressure.

(a) at the brain (the pressure is enough to perfuse the brain with blood, to keep the giraffe from fainting)

(b) at the feet (the pressure must be countered by tight-fitting skin acting like a pressure stocking).

(c) If the giraffe were to lower its head to drink from a pond without splaying its legs and moving slowly, what would be the increase in the blood pressure in the brain? (Such action would probably be lethal.)

1) Pm₂ = 1.9 10⁴ Pa, b) P_feet = 5.4 10⁴ Pa, c) Pm₄ = 4.4 10⁴ Pa

Explanation:

a) Pressure can be found using Bernoulli's equation

P₁ + ½ rho v₁² + rho g y₁ = P₂ + ½ rho v₂² + rgo g y₂

The amount of blood that runs through the constant system, all the blood that reaches the brain leaves it, so we can assume that the speed of entry and exit of the total blood is the same. In this case the equation is

P₁-P₂ = rgo h (y₂-y₁)

The gauge pressure is

Pm = P₁ - P₂

Pm₂ = 1.06 10³ 9.8 1.83

Pm₂ = 19 10³ Pa

Pm₂ = 1.9 10⁴ Pa

The pressure in the heart is

Pm₁ = 246 torr (1,013 10⁵ Pa / 760 torr) = 3,279 10⁴ Pa

Therefore the gauge pressure is an order of magnitude less

Total or absolute pressure is

Pm₂ = P_heart - P_brain

P_brain = P_heart - Pm₂

P brain = 3,279 10⁴ - 1.9 10⁴

P brain = 1.4 104 Pa

b) on the feet

Pm₃ = rho g y₃

y = 2.04 m

Pm₃ = 1.06 10³ 9.8 2.04

Pm₃ = 21 10³ Pa

Pm₃ = 2.1 10⁴ Pa

Total pressure

Pm₃ = P_feet + P_heart

P_feet = Pm₃ + P_heart

P_feet = 3,279 10⁴ + 2.1 10⁴

P_feet = 5.4 10⁴ Pa

c) If you lower your head the height change is

h = 1.83 + 2.04

h = 4.23 m

Pm₄ = 1.06 10³ 9.8 4.23

Pm₄ = 4.4 10⁴ Pa