How is Maximum Height Determined in Unsteady Fluid Flow into a Cylinder?

[hem1ngway]

Hey this problem of mine involves unsteady fluid flow (Q) into a cylinder of diameter (D). There is a small hole at the bottom of the cylinder of diameter (d) which is much smaller than (D) hence d << D. Because of this the fluid level will rise to a maximum height (h) before decreasing to zero over time.

Please see diagram

http://img407.imageshack.us/img407/8462/pic1ub8.th.jpg

How does the unsteady fluid flow relate to the height? As in is it possible to work out this maximum height that would occur?





I'm so stuck on this! Could anyone point me in the right direction? I understand that the work will not be done for me but if you could point me in the right direction with equations to use I would be very greatful.

 

[Brian_C]

Why would the fluid level decrease to zero? The fluid level should reach a steady state when the flow rate through the smaller hole becomes equal to the flow rate into the cylinder. The velocity of the fluid issuing from the smaller hole should increase as the static pressure increases. If you assume an inviscid incompressible flow, you can derive a relationship between this velocity and the fluid height from Bernoulli's principle.

 

[hem1ngway]

The fluid level would eventually decrease to zero over time as it would flow out of the smaller diameter at the bottom of the cylinder due to gravity.

When the flow rate into the cylinder equals the flow rate out of the cylinder a height of fluid will occur.

How do I work out that height of fluid and relate it to the flow rate into and out of the cylinder?

 

[Brian_C]

To find the flow rate out of the cylinder, you need to know the velocity of fluid issuing from the small hole. To do this, you will need to apply Bernoulli's equation to the fluid issuing from the smaller hole.

As you may recall, Bernoulli's equation states that the sum of the static and dynamic pressures is constant along a fluid steam. What are the static and dynamic pressures in the fluid just before reaching the small orifice? What are the static and dynamic pressures in the fluid issuing from the small orifice?