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Solved University-Physics Problems

Physics 2.-  Fluid Static

 

Javier Montenegro Joo

jmj@VirtualDynamics.Org

 

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  Fluid Static.-  
     
 

(1) An open U-shaped tube has branches of section  A and, it contains a liquid of a certain density.  Determine the volume of another liquid having a density which is half the density of the first liquid, which must be poured in a branch of the tube so that the first liquid rises ho  in the other branch.  Both liquids are immiscible.

Solution.-

The figure shows the two acts of this problem:  In the first act appears only the first liquid. In the second act, the second liquid has been poured in the left branch of the tube, being h  the height of this second fluid. For the first liquid to raise a height ho in the right hand branch, the interface level must descend  ho  in the left branch. Under these conditions, at the level of the interface, the pressure is the same in both branches:

 
     
 

(2)    A 0.50 kg object weighs 1.50 N in water and 0.70 N in petroleum. Determine the density of the petroleum.

Solution.-

The upthrust or buoyancy E is the real weight minus the apparent weight of the object in the fluid:

 
     
 

 

 
     
 

 (5) A long hose containing two immiscible liquids is vertically bent as shown in the sketch. A piston is making a pressure Po at the left extreme of the hose, while the extreme at the right side is closed with a stopper.  Determine the pressure at the stopper.

Solution .-

Note that when varying the pressure Po exerted by the piston at the left extreme of the hose, the pressure changes along the entire system, hence in order to find the pressure at any point, the connected pressures starting at the left extreme must be considered.  Bear in mind that at the level of two contiguous interfaces the pressure is the same. If the piston were retired the pressure at its position would be that of the atmosphere.

 
     
 

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