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Q11P

Expert-verifiedFound in: Page 407

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**Giraffe bending to drink. In a giraffe with its head ${\mathbf{2}}{\mathbf{.}}{\mathbf{0}}{\mathbf{}}{\mathit{m}}$ above its heart, and its heart ${\mathbf{2}}{\mathbf{.}}{\mathbf{0}}{\mathbf{}}{\mathit{m}}$ above its feet, the (hydrostatic) gauge pressure in the blood at its heart is250 ${\mathit{t}}{\mathit{o}}{\mathit{r}}{\mathit{r}}$. Assume that the giraffe stands upright and the blood density is ${\mathbf{1}}{\mathbf{.}}{\mathbf{06}}{\mathbf{\times}}{{\mathbf{10}}}^{{\mathbf{3}}}{\mathit{k}}{\mathit{g}}{\mathbf{/}}{{\mathit{m}}}^{{\mathbf{3}}}$ . (a) In ${\mathit{t}}{\mathit{o}}{\mathit{r}}{\mathit{r}}$ (or role="math" localid="1657260976786" ${\mathit{m}}{\mathit{m}}{\mathbf{}}{\mathit{H}}{\mathit{g}}$), find the (gauge) blood pressure at the brain (the pressure is enough to perfuse the brain with blood, to keep the giraffe from fainting). (b) ${\mathit{t}}{\mathit{o}}{\mathit{r}}{\mathit{r}}$ In (or ${\mathit{m}}{\mathit{m}}{\mathbf{}}{\mathit{H}}{\mathit{g}}$), find the (gauge) blood pressure at the feet (the pressure must be countered by tight-fitting skin acting like a pressure stocking). (c) If the giraffe were to lower its head to drink from a pond without splaying its legs and moving slowly, what would be the increase in the blood pressure in the brain? (Such action would probably be lethal.)**

- Gauge pressure at the brain of giraffe is $94torr$
- Gauge pressure at the feet of giraffe is $406torr$
- Increment in pressure is 312 $torr$

- Density of blood, $p=1.06\times {10}^{3}kg/{m}^{3}$
- Heart pressure, $p=250torr$

**Use the formula for gauge pressure, which depends on density, height, and acceleration due to gravity. Gauge pressure is that, which is exerted by a fluid at any point of time at equilibrium due to the force applied by gravity.**

Formula:

Pressure applied on a fluid surface, $p=pgh$

Net pressure applied on a body, $\u2206p={p}_{2}-{p}_{1}$

From equation (ii), the pressure at brain can be given as:

${p}_{brain}={p}_{heart}-pgh\phantom{\rule{0ex}{0ex}}=250-1.06\times {10}^{3}\times 9.8\times 2\times \frac{1torr}{133.33Pa}(\because 1torr=133.33Pa)\phantom{\rule{0ex}{0ex}}=94.2torr$

The pressure at brain is 94.2 torr.

From equation (ii), the pressure at brain can be given as:

${P}_{feet}={P}_{heart}+pgh(\because \mathrm{here}\mathrm{pressure}\mathrm{is}\mathrm{total}\mathrm{pressure})\phantom{\rule{0ex}{0ex}}=250+1.06\times {10}^{3}\times 9.8\times 2\times \frac{1torr}{133.33Pa}(\because 1torr=133.33Pa)\phantom{\rule{0ex}{0ex}}=405.8torr$

The pressure at feet is 405.8 torr.

From equation (ii), the net pressure between brain and feet can be given as:

$\u2206p={p}_{brain}-{p}_{feet}\phantom{\rule{0ex}{0ex}}=405.8-94.2\phantom{\rule{0ex}{0ex}}=311.6torr$

Hence, the increased value of pressure is 311.6 torr.

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