How Deep Could Tarzan Dive While Breathing Through a Reed?

[Soaring Crane]

Ape Man in a movie is shown evading his captors by hiding underwater for many minutes while breathing through a long reed. Assuming the maximum pressure difference lungs can manage and still breathe is -80 mm-Hg , calculate the deepest he could have been.

I immediately thought of P = p*g*h, where p = density. h is the depth, but this is for gauge pressure. Do I use the formula for absolute pressure P = atmospheric pressure + pgh?

Am I correct in my reasoning?

Thanks.

 

[vincentchan]

First... you have to make an assumtion that the lung won't be compress under water, otherwise the problem can't be solve this way.
Yes the absolute pressure under water is $\rho g h + 1atm$... however, the pressure inside the (uncompressed) lung is 1atm... so the DIFFERENT of the pressue is $\rho g h$

 

[wais]

Yes, you are correct in your reasoning. The formula for absolute pressure, P = atmospheric pressure + pgh, should be used in this scenario. This is because the maximum pressure difference that the lungs can manage is already taking into account the atmospheric pressure. So, to calculate the depth at which the ape man could have been hiding, we would use the formula P = atmospheric pressure + pgh, where P = -80 mm-Hg and p = density of the fluid (water in this case). Solving for h, we get h = -P/(pg) = -(-80 mm-Hg)/((1000 kg/m^3)(9.8 m/s^2)) = 0.0082 m. This means that the deepest the ape man could have been hiding is approximately 8.2 cm below the surface of the water. This is assuming that the ape man's lungs are able to handle a pressure difference of -80 mm-Hg without any harm.

 

[wais]

Yes, you are correct in your reasoning. In this scenario, we can assume that the atmospheric pressure is equivalent to 0 mm-Hg since Tarzan is underwater. Therefore, the formula for absolute pressure, P = atmospheric pressure + pgh, would be more appropriate to use in this case.

To calculate the maximum depth Tarzan could have been at, we can rearrange the formula to solve for h:

h = (P - atmospheric pressure)/(p*g)

Substituting the given values, we get:

h = (-80 mm-Hg - 0 mm-Hg)/(density of air * 9.8 m/s^2)

Since the density of air is approximately 1.2 kg/m^3, we can convert the units to get:

h = (-80 mm-Hg - 0 mm-Hg)/(1.2 kg/m^3 * 9.8 m/s^2)

h = -80 mm-Hg / 11.76 kg/m^3 * m/s^2

h = -6.8 m

Therefore, Tarzan could have been at a maximum depth of 6.8 meters while still being able to breathe through the reed with a pressure difference of -80 mm-Hg in his lungs. Any deeper than that and the pressure would be too great for him to manage and breathe.

It's amazing to think about the capabilities of the human body and how it can adapt to different environments and situations. This scene from the movie showcases Tarzan's survival skills and his ability to think quickly under pressure (no pun intended).