Question

(a) Calculate the difference in blood pressure between the feet and top of the head for a person who is 1.75 m tall.
Pa

(b) Consider a cylindrical segment of a blood vessel 3.75 cm long and 2.00 mm in diameter. What additional outward force would such a vessel need to withstand in the person's feet compared to a similar vessel in her head?
N

Answer 1

Given Data

h =1.75 m

diameter =2.00 mm = 2*10^-3 m ==> Radius = ( 2*10^-3 m)/2 = 1*10^-3 m

Length = 3.75 cm = 3.75*10^-3 m

We have

Average density of blood , rho = 1.06 x 10³kg/m³

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a) The difference in blood pressure is

Delta P = rho * g* h

           = 1.06 x 10³kg/m³ * 9.8 m/s^2 * 1.75

           = 18179 Pa --> Answer

b) Additional outward force vessel needed to withstand in the person's feet is

Delta F = Delta P * A

            = Delta P * (2Pi*r*l)

           = 18179 * 2Pi* (1*10^-3)*(3.75*10^-2)

           = 4.28 N --> Answer