How Long Does It Take to Empty a Tube Using Bernoulli's Equation?

[domjoly1985]

Hi, I have a problem involving involving Bernoulli's equation and the emptying of a tube of liquid over time, I will outline the problem and then the question...

There is a vertical tube, which narrows into smaller tube part of the way down, it is filled with an inviscid, incompressible and irrotational fluid. The bottom/outlet of the tube is at z=0, where the cross-sectional area is represented by A0 and the fluid's speed by q1. The top of the tube is at z=1, the top level of the liquid is at h(t), where t is time, the cross-sectional area of the liquid level is A1 and the speed it is falling at is q0. The pressure is the same at both ends of the tube.

I need to find out how long it takes for the tube to empty under gravity, using Bernoulli's equation, and assuming the flow is approximately steady.
Any help would be appreciated, if any more information is required I will reply asap. Thanks

 

[radou]

Present your ideas/efforts.

 

[domjoly1985]

Ive been able to get the speed of the liquid coming out of the bottom of the tube, but I have no idea where to start concerning it's emptying time.

 

[Repetit]

If you have determined the speed of the liquid when it comes out of the tube and you know the cross sectional area of the outlet you can determine the volume flowrate out of the tube (q1*A0). Then you know how much volume of liquid exits the tube per second and you can use this information to determine the emptying time.

 

[domjoly1985]

I realize that but to do it.

 

[Repetit]

If the total liquid volume is V the emptying time is V/Q where Q is the volume flow rate out of the tube.