Chapter 13: Liquids

 


The atoms or molecules in liquids have a strong attraction for each other, but the forces holding them together do not hold them in fixed positions relative to each other, but rather they can "slide past" each other and easily change the shape of the liquid.


Pressure

 

PB – PA = Dgh

Where g = 10m/s2 on the earth. If the liquid is water, D = 1,000kg/m3, and the height difference is 2m, the pressure at B is 20,000N/m2, or 20,000Pa, greater than the pressure at A.

One way of understanding this is to note that the fluid at B must support the weight of the material above it, and there is more material above B than above A.


Buoyancy


Pascal's Principle

Pascal's principle says that if I increase the pressure by Pinc on one part of a liquid in an enclosed container, the pressure everywhere in the liquid will increase by the same amount, Pinc.  In the figure at the right, the pressure under the piston, i.e. the plunger, was simply the air pressure, 105Pa..  At the bottom of the container it was 1.5x105 Pa because of the variation of pressure with depth.  When I push on the piston, of area 0.01m2, with a force of 200N, I increase the pressure under the piston by Pinc = Force/Area = 2x104Pa.  Then the pressure just under the piston becomes P = 105Pa + Pinc = 1.2x105Pa.  The pressure at the bottom will also increase by 2x104Pa and become 1.7x105Pa.

This effect is used in hydraulic systems (power steering, brakes etc.)  It allows us to amplify force, but not work!  The typical arrangement is to have two pistons of different areas as shown at the right.  The left piston has an area of 0.01m2 and the right one and area of 0.05m2.  If I place a 5kg mass (weight = 50N) on the left piston, the pressure will increase by 5x103Pa.  It will also increase by 5x103Pa under the right one.  This produces an extra force on the right piston of 5x103Pa x 0.05m2 = 250N.  Note that for the two forces to "balance", Fleft/Aleft = Fright/Aright , i.e. the two pressure changes must be equal.


Cohesion and Adhesion