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By means of physiological adaptations that are still not very well understood, sperm whales are thought to be able to hunt for their food at depths of between 400 $\mathrm{m}$ and 3000 $\mathrm{m.}$ (a) What range of gauge pressures (in Pa and atm) do the whales withstand at these depths? (b) Estimate the total inward force of water pressure on the surface of a sperm whale at a depth of $3000 \mathrm{m},$ modeling the whale as a cylinder 16 $\mathrm{m}$ long and 4 $\mathrm{m}$ in diameter.

a) $4\times 10^6 atm; 40atm$.b) $7 \times 10^{9} N$

Physics 101 Mechanics

Chapter 13

Fluid Mechanics

Temperature and Heat

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

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Okay. So first of all in this problem, we have to calculate what is the gauge pressure that the whales will stand at the steps. So let's see the gauge pressure. That's remember what it is doubt, uh, is going to be equal density off the liquid, which in this case, is seawater. Uh, multiply by whole horde G age, the gravity acceleration and the depth. That is that that the bill that the way yours are so we can calculate this in Moscow first. So this is going to be, ah 1.3 which is a density off the seawater 1.0 tree times 10 to the tree that multiplies gravity acceleration of nine point eight. The multiplies that Rijs 400 meters. So if we calculate this in Pasco first we have a gauge pressure off for times 10 for this six Lasko. Okay, so But we want this answer in Pasco in the team A spheres. So we have to change. This is the first answer. Now the skull cledus a team, a sphere. So entity atmospheres. We have to trust form if Basco timbers freezing how we do this? We divided by war points leader one times 10 to the five. Therefore, you forgot Cletus. We have something close to 40. A team was fierce. So that is the gauge. Pressure ting the hemispheres. Any Posco's. Now let's look to the second I tell of this problem. So in the second item, we have to calculate what should be the force in work that will. You suffers at a depth off 3000 meters and we have to consider that the way or is a cylinder. So Okay, that's we're all here. What the problem actually wants. We have a cylinder here just going to be or wail. And since the way or is underwater, the Wales suffers forces in all directions pressure in all directions. And since we have pressure, we can calculate the force because we know that force is just pressure the multiplies d surface area. And since we want to consider the way you as a cylinder, let's go, Khalid. First the surface area off the cylinder. It's going to be the surface area of both circles. So is true. Times by are square plus the area off the shower of this lender riches, uh, to buy. Oh, are l which is the length off the cylinder. Okay, So if recalculate this measurements that the problem gives us, we're going to have that. The surface area off the whale is to fi. They're multiplies to square. What sport here without a parenthesis by to square plus to buy to they're multiplies the lens, which is 16 meters. So calculating all this. We have a surface area off 226 meters. You square. So now that we have the surface area, we can finally calculate the inward force that this way you, sir. First, which is going to be Let's see, um, And if pressure is just three times 10 to the seven Moscow and multiplies the surface area off 2 to 6. So if you are Cletus, we have inward force off seven times 10 Jordan lying new tunes. And that's actually define our answer to this problem. Thanks for watching

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