Physics I Chap 15.Fluid Statics Prof. WAN, Xin

Density Density (scalar): mass of a small element of material  m divided by its volume  V –For infinitesimally small  V:  =  m /  V –For homogeneous material:  = m / V

Water Bed F The mattress of a water bed is 2.00 m long by 2.00 m wide and 30.0 cm deep. (a) Find the weight of the water in the mattress. F The density of water is kg/m 3, and so the mass of the water is F and its weight is About the weight of a compact car!

Pressure F Under static condition, force acts normal or perpendicular to the surface – vector. F Pressure: the magnitude of the normal force per unit surface area – scalar.

Water Bed (Continued) F (b) Find the pressure exerted by the water on the floor when the bed rests in its normal position. Assume that the entire lower surface of the bed makes contact with the floor. F When the bed is in its normal position, the cross- sectional area is 4.00 m 2

Common Units

Origin of Pressure F Microscopic origin: collisions of molecules of the fluid with the surface –Action and reaction: Newton’s third law liquid f reaction Wall

Bulk Modulus F Can density describe the resistance of a fluid to compression? Why? F For a fixed temperature, –Define: bulk modulus –Pressure change  p –Fractional change in volume  V/V

Bulk Modulus F Solids & liquids –Large B, ~ 10 9 N/m 2 –(Practically,) incompressible F Gases –Small B, ~ 10 5 N/m 2 –Easily compressible

Pressure in a Fluid at Rest y y+dy A pA (p+dp)A (dm)g

Pressure in a Fluid at Rest  Assumption: , g independent of y

Mercury Barometer F How to measure atmospheric pressure? F E. Torricelli ( ) For mercury, h = 760 mm. How high will water rise? No more than h = p atm /  g = 10.3 m h p atm p=0 Vacuum!

Atmospheric Pressure  Gases are compressible. Thus,  varies! dy

Atmospheric Pressure

A.P. – an Improved Version Temperature decreases 6 o C for each 1,000 meters of elevation

A.P. – an Improved Version

Temperature Corrections

Q & A: On Pressure Q : Is it possible to stand on the roof of a four-story (12 m) building and drink, using a tube, from a glass on the ground? 12 m

A : Even if a person could completely remove all of the air from the tube, the height to which the outside air pressure pushes the water up the straw would not be high enough for him/her to drink the water, no matter how hard he/she sucks! Really? Q & A on Pressure 12 m

Moorea, French Polynesia

Snorkeling

Blaise Pascal Blaise Pascal ( ) French mathematician & philosopher; founder of modern theory of probability; discovered Pascal's law of pressure and principle of the hydraulic press.

Pascal’s Principle Pressure applied to an enclosed fluid is transmitted undimished to every portion of the fluid and to the walls of the containing vessel. F p d p ext

Hydraulic Lever FiFi mg AiAi AoAo FoFo didi dodo

Hydraulic Brake Fred Duesenberg originated hydraulic brakes on his 1914 racing cars and Duesenberg was the first automotive marque to use the technology on a passenger car in In 1918 Malcolm Lougheed (who later changed the spelling of his name to Lockheed) developed a hydraulic brake system.

Archimedes of Syracuse Archimedes (circa B.C.) Greek mathematician & inventor known especially for work in mechanics; discovered principle of buoyancy; wrote on volumes of spheres and cylinders, value of , etc.

Archimedes of Syracuse Give me a place to stand and I will move the earth.

Archimedes’ Principle A body wholly or partially immersed in a fluid is buoyed up by a force equal in magnitude to the weight of the fluid displaced by the body. FBFB mg

Two Comments F Buoyant force  volume/density F Center of buoyancy (not fixed) Center of gravity

Q&A: Galileo’s Scale F Can you invent a scale that one can use to read the percentage of silver in the gold crown (let’s say, to help Archimedes to determine the exact percentage) without explicit calculations?

Eureka