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A viscous, incompressible fluid, flows slowly from a cylindrical container of diameter into a horizontal capillary tube of diameter and length .
We neglect the effects due to the tube ends.
Can we consider the flow as quasi-permanent ? Justify.
Deduce the expression of the volume flow rate as a function of .
We place ourselves in the ARQS.
One has a cylindrical Poiseuille flow :
The liquid is practically at rest in the container of diameter .
We can therefore write the fluid static law :
Establish a differential equation satisfied by .
Solve for the initial condition .
The flow is incompressible, there is conservation of volume flow rate :
This leads to the differential equation :
Whose solution is :
It took a duration so that the liquid level moves from the height to the height .
Determining the kinematic viscosity of the liquid.
It gives : , , and
Numerical application gives :