A person of height 1.65 ,m is standing uprigh | vedclass

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Question

(A) The pressure difference between the head and the feet is given by $\Delta P = ho gh$. Here, $ho = 1.1 	imes 10^3 \,kg \,m^{-3}$, $g = 10 \,ms

Vedclass · Accepted Answer

$0.57$

Vedclass · Answer

(A) The pressure difference between the head and the feet is given by $\Delta P = ho gh$. Here, $ho = 1.1 	imes 10^3 \,kg \,m^{-3}$, $g = 10 \,ms^{-2}$, and $h = 1.65 \,m$. $\Delta P = 1.1 	imes 10^3 	imes 10 	imes 1.65 = 1.815 	imes 10^4 \,Pa$. The force $F$ required to balance this pressure on the blood vessel is $F = \Delta P 	imes A$, where $A$ is the surface area of the blood vessel. The blood vessel is a cylinder with length $L = 1 \,cm = 10^{-2} \,m$ and diameter $d = 1 \,mm = 10^{-3} \,m$ (radius $r = 0.5 	imes 10^{-3} \,m$). The surface area $A$ (lateral surface area) is $A = 2 \pi r L$. $A = 2 	imes 3.14159 	imes 0.5 	imes 10^{-3} 	imes 10^{-2} = 3.14159 	imes 10^{-5} \,m^2$. $F = (1.815 	imes 10^4) 	imes (3.14159 	imes 10^{-5}) \approx 0.57 \,N$.

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