Question

Your heart pumps blood at a pressure of 100 mmHg and flow speed of 60 cm/s. At your brain, the blood enters capillaries with such a large total cross-sectional area that the blood velocity is much smaller: about 0.7 mm/s. Ignore viscosity in the capillaries. How long could your neck be so that blood still reaches your brain in m

Answer 1

Answer:

1.28 m

Explanation:

Generally, pressure of fluid is given by

$P=\rho g h$ where g is acceleration due to gravity, h is the height and $\rho$ is the density

Considering that the pressure for mercury is same as for blood only that the height and density of fluid are different then

$\rho_b g h_b= \rho_m g h_m$

Since g is constant, then

$\rho_b h_b= \rho_m h_m$

Making $h_b$ the subject of the formula then

$h_b=\frac {\rho_m h_m}{\rho_b}$

Where subscripts m and b denote mercury and blood respectively

Assuming density of blood is 1060 Kg/m3, density of mercury as 13600 Kg/m3 and substituting height of mercury for 0.1 m then

$h_b=\frac {13600*0.1}{1060}=1.283018868  m \approx 1.28 m$