1-) A less-dense liquid of density ? 1 floats on top of a more-dense liquid of d

Question

1-) A less-dense liquid of density ?1 floats on top of a more-dense liquid of density ?2. A uniform cylinder of length l and density ?, with ?1<?<?2, floats at the interface with its long axis vertical. What fraction of the length is in the more-dense liquid? Express your answer in terms of the given quantities.

2-) Water flows from the pipe shown in the figure with a speed of 7.0m/s.

A-) What is the water pressure as it exits into the air?

B-) What is the height h of the standing column of water?

Explanation / Answer

Let the cross sectional (end) surface area be A.

Total Volume of the cylinder = V = ?*A*l

Suppose length l1 is immersed in the lighterliquid while length l2 is immersed in the denserliquid.

So, volume immerseed in the lighter liquid isV1 = ?*A*l1

Volume immersed in the denser liquid is V2 =?*A*l2

Buoyant forces actinbg due to immersiuon in the twoliquids are :

F1 = V1*?1*g

F2 = V2*?2*g

So, F1 + F2 = W = V*?*g inorder to balance the weight of the cylinder.

Now, V = V1+V2 and thus l =l1 + l2

So, Ag*[l1?1 +l2?2] = Ag*l?

and l1+l2=l

=> l1 = l-l2

=> (l-l2)*?1 +l2*?2 = l?

=>l2*(?2-?1) =l(?-?1)

=> l2 = l(?-?1)/(?2-?1)

Hence this is the length immersed in the denserliquid.

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