Pressure and density in swimming.

AI Thread Summary
The discussion revolves around determining how deep a diver can swim using a snorkel, given that the pressure difference between the inside and outside of the lungs must not exceed 1/21 of an atmosphere. The relevant equation for calculating pressure at a certain depth is pgh, where p is the water's density (1042 kg/m3), g is gravitational acceleration, and h is the depth. The pressure limit of 1/21 atm converts to approximately 4824 Pascals, which needs to be equated to the pressure exerted by the water at depth. Participants express uncertainty about how to apply these concepts to find the maximum depth the swimmer can reach. The conversation highlights the need for clarity in unit conversions and the application of pressure equations in fluid dynamics.
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Homework Statement


The human lungs can function satisfactorily up to a limit where the pressure difference between the outside and inside of the lungs is 1/21 of an atmosphere. If a diver uses a snorkel for breathing, how far below the water can she swim? Assume the diver is in salt water whose density is 1042 kg/m3.

Homework Equations


The Attempt at a Solution


I think pgh, where p is density, g is gravitational acceleration, and h would be the height. I think the height would tell you how far the swimmer could go below water. I'm honestly not exactly sure where to start this one!
 
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That pressure has to be equal to 1/21 atm right? Remember the units are going to be different and account for that.
 
I converted the 1/21 atm to 4824 Pascals. I am still not sure how to find the height below the water the swimmer can go though?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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