Final answer:
The gauge pressure at the brain of a giraffe, which is 2 meters above its heart, can be calculated using hydrostatic pressure principles and is found to be approximately 95.6 torr.
Step-by-step explanation:
To calculate the gauge pressure in the giraffe's brain, you need to consider the hydrostatic pressure due to the height difference between the heart and the brain.
If the gauge pressure at the heart is 250 torr, and assuming there is no loss of pressure due to resistance (which is a reasonable assumption in major arteries), you can calculate the pressure at the brain using the following formula derived from hydrostatic pressure principles:
Pressure at brain = Pressure at heart - (ρ * g * h)
where ρ is the density of the blood (which, in the question, is missing and therefore we'll assume a typical value of 1050 kg/m³), g is the acceleration due to gravity (9.8 m/s²), and h is the height difference (2 meters in this case).
Using the values:
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- Density of blood, ρ = 1050 kg/m³
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- Acceleration due to gravity, g = 9.8 m/s²
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- Height difference, h = 2 m
First, convert torr to pascals since 1 torr = 133.322 Pa:
Pressure at heart in Pa = 250 torr * 133.322 Pa/torr
≈ 33330.5 Pa
Now, calculate the pressure change due to the height difference:
ΔP = ρ * g * h = 1050 kg/m³ * 9.8 m/s² * 2 m
= 20580 Pa
So, pressure at the brain in Pa = 33330.5 Pa - 20580 Pa
= 12750.5 Pa
Lastly, convert this pressure back to torr:
Pressure at the brain in torr = 12750.5 Pa / 133.322 Pa/torr
≈ 95.6 torr
The gauge pressure at the brain would therefore be approximately 95.6 torr.