Question

When a pilot takes a tight turn at high speed in a modern fighter airplane, the blood pressure at the brain level decreases, blood no longer perfuse the brain, and the blood in the brain drains. If the heart maintains the (hydrostatic) gauge pressure in the aorta at $\mathbf{120}\mathbf{}\mathit{t}\mathit{o}\mathit{r}\mathit{r}$(or $\mathit{m}\mathit{m}\mathbf{}\mathit{H}\mathit{g}$) when the pilot undergoes a horizontal centripetal acceleration of$\mathbf{4}\mathit{g}$. What is the blood pressure ($\mathit{i}\mathit{n}\mathbf{}\mathit{t}\mathit{o}\mathit{r}\mathit{r}$) at the brain, localid="1657253735468" $\mathbf{30}\mathbf{}\mathit{c}\mathit{m}$radially inward from the heart? The perfusion in the brain is small enough that the vision switches to black and white and narrows to “tunnel vision” and the pilot can undergo g-LOC (“g-induced loss of consciousness”). Blood density is$\mathbf{1}\mathbf{.}\mathbf{06}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathit{k}\mathit{g}\mathbf{/}{\mathit{m}}^{\mathbf{3}}$.

Short answer

The blood pressure (in torr) at the brain,$30cm$ radially inward from the heart isrole="math" localid="1657252498313" $26.5torr$

Step-by-step solution

The given data

1. The heart maintains the gauge pressure in the aorta at$p_{heart}=120torr$
2. Pilot undergoes centripetal acceleration,$a=4g$
3. Depth,$h=0.30m|$
4. Density of blood, $\mathrm{\rho }=1.06\times {10}^3\frac{kg}{m^3}$

Understanding the concept of pressure

Using the formula of hydrostatic pressure, we can find theblood pressure (in torr) at the brain,radically inward from the heart.

Formula:

Net pressure on the part of brain, $p_{brain}=p_{heart}-\mathrm{\rho }gh$ (i)

Calculation of net blood pressure

Using equation (i) and the given values, we get

$$\begin{gathered} p_{brain}=120torr-\left(1.06\times {10}^3\frac{kg}{m^3}\right)\left(4\times 9.8\frac{m}{s^2}\right)(0.30)\frac{1torr}{133.33Pa}(\because 1\mathrm{torr}=133.33\mathrm{Pa}) \\ =120torr-93.5torr \\ =26.5torr \end{gathered}$$

Therefore,the blood pressure (in torr) at the brain,radically inward from the heart is$26.5torr$