Physics Fluid Dynamics

Question

Suppose that a person afflicted with aneurysm has enlarged portion of aorta with a cross

sectional area 50% bigger than the normal. What is the speed of the blood through this

enlarged portion? What is pressure difference between the normal and enlarged aorta?

Assume that the speed of blood in the normal aorta is 40cm/s and that the person is lying

down.

Answer 1

WE have Bernully equation for horizontal tube: p₁ + ρv₁²/2 = p₂ + ρv₂²/2.

Now v₁A₁ = v₂A₂; A₂ = 1.5A₁, v₁ = 1.5v₂; v₂ = 40cm/s/1.5 = 26.67 cm/s

p₂ - p₁ = ρ/2(v₁² - v₂²) = 1000kg/m³/2(0.4²m²/s² - 0.2667²m²/s²) = 44.44 Pa