Question

A healthy adult of height 1.7 m has an average blood pressure (BP) of 100mm of Hg. The heart is typically at a height of 1.3m from the foot. Take the density of blood to be ${10^3}kg/{m^3}$ and note that 100mm of Hg is equivalent to 13.3 KPa (KiloPascal). The ratio of blood pressure in the foot region to that in the head region is close to:
(a) one
(b) two
(c) three
(d) four

Answer 1

Hint: In this question find the height of head from the heart using the total height of man as 1.7 m and the height of heart being given as 1.3m. Then use the direct formula that the pressure at any point with respect to a given point is given as $\left( {\rho gh} \right)$ where h is the distance of that point w.r.t. the given point. This will help get the right answer.

Formula used – $\left( {\rho gh} \right)$

Complete Step-by-Step solution:
Given data:
Pressure at heart level is 100 mm of Hg = 13.3 kPa.
Height of an adult (h) = 1.7 m.
Height of heart from the foot of man ${h_1}$ = 1.3 m
Therefore height of head from the heart ${h_2}$ = 1.7 – 1.3 = 0.4 m
Density $\left( \rho \right)$ of blood = ${10^3}$ kg/m3.
Use acceleration of gravity (g) = 9.8 m/$s^2$.
Now as we know that the pressure at any point w.r.t. the given point = $\left( {\rho gh} \right)$, where h is the distance of that point w.r.t. the given point.
Now pressure at foot is the sum of pressure at heart and the $\left( {\rho g{h_1}} \right)$
So the pressure at the foot is
$ \Rightarrow {P_{foot}} = 13.3 \times 1000 + {10^3}\left( {9.8} \right)\left( {1.3} \right)$
$ \Rightarrow {P_{foot}} = 26.04$ Kpa.
Now the pressure at the head is the difference of pressure at heart and the $\left( {\rho g{h_2}} \right)$
So the pressure at the head is
$ \Rightarrow {P_{head}} = 13.3 \times 1000 - {10^3}\left( {9.8} \right)\left( {0.4} \right)$
$ \Rightarrow {P_{head}} = 9.38$ Kpa.
So the ratio of blood pressure in the foot region to that in the head region is
$ \Rightarrow \dfrac{{{P_{foot}}}}{{{P_{head}}}} = \dfrac{{26.04}}{{9.38}} = 2.776 \simeq 3$
So this is the required answer.
Hence option (C) is the correct answer.

Note – In this question the trick point was that in question the conversion of 100mm of Hg in kilopascal is given and this is actually the pressure at heart level that is 100 mm of Hg. The key here is that the while calculating pressure at foot we have added the heart pressure and while calculating pressure at head we have subtracted the pressure of heart, this concept is somewhat similar to the fact that pressure at depth of the sea is greater as compared to the surface, so when heart pumps blood towards foot the pressure has to be more, however when heart pumps it to head the pressure will be less.