How quickly will a can sink in water with a small hole at the bottom?

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The discussion focuses on determining the sinking speed of a cylindrical can with a small hole at the bottom when immersed in water. The main equation derived is dy/dt = (a/A)sqrt(2gy), which relates the rate of change of depth to the hole's area and the can's base area. A participant expresses difficulty in obtaining the correct answer and questions whether the increasing pressure inside the can has been adequately considered. Suggestions are made to clarify the justification for the equations used in the calculations. The conversation emphasizes the importance of accounting for pressure changes in fluid dynamics when solving the problem.
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Homework Statement



A cylindrical can of height h and base area A is immersed in water to a depth ho and left to sink down. A small hole of area 'a' exists at the bottom of the base of the can. Determine how quickly the can sinks.
http://img80.imageshack.us/my.php?image=fluids1wb7.jpg

Homework Equations


http://img178.imageshack.us/my.php?image=fluidssolmz5.jpg
Thus, vo = sqrt(2gy)
AV = avo
V: velocity of fluid w.r.t. the container

The Attempt at a Solution



Thus,
dy/dt = (a/A)sqrt(2gy)
or, dy/sqrt(y) = (a/A) sqrt(2g) dt
or, on integrating from ho to h, i get

t = sqrt(2/g)[sqrt(h) - sqrt(ho)]A/a

I am not getting the answer, where did i go wrong.
 
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In your diagram, y is shown to be the depth of the bottom of the can from the water surface. Have you taken into account that the pressure inside the can will also increase as the water flows in, thus decreasing the rate of water flow inside. Maybe you have, but why don't you just write the justification for your equation?
 
ah.. thx.. i didn't do that.. i will try to work it out again...
 
i m not able to do ... can you help me with the solution pls
 
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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