A cylindrical tube that is 2.50 m long and has a radius of 150 mm is filled with

Question

A cylindrical tube that is 2.50 m long and has a radius of 150 mm is filled with water. It is oriented with its long central axis vertical, and it is open to the air at the upper end. A hole 80.0 mm in radius is drilled in the bottom, and the water is allowed to drain out.

A) When the water level is half the height of the tube what is the speed of the water exiting though the hole?

B) At what rate (in meters cubed per second) is the water leaving the tube?

C) How fast is the top of the water column falling?

Explanation / Answer

A) when it will become half of initial height.

AVh=?r2(h2-h1)

?[(0.08)^2]*Vh=?[(0.15)^2]*(2.50-1.25)

Vh=4.3945m/s

B) rate (in meters cubed per second) is the water leaving the tube=AV=?[(0.08)^2]*4.3945=0.08836m3/s

C)Continuity equation

A1Vt=A2Vh

?[(0.15)^2]Vt=?[(0.08)^2]*Vh

Vt=(64/225)Vh

Vt=64/225*4.3945=1.25m/s

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