Force in Fluid Systems

4 states of matter Flip chart activity Flip chart activity Flip chart activity Flip chart activity Solid Solid Liquid Liquid Gas Gas Plasma Plasma

Fluids A fluid can be a liquid or a gas A fluid can be a liquid or a gas

Hydraulic Systems A fluid system that uses a liquid as the fluid A fluid system that uses a liquid as the fluid

Pneumatic A fluid system that uses a gas as the fluid A fluid system that uses a gas as the fluid

Density See page 30 for the Density Table 1.4 Density = mass / volume Density = mass / volume Ex : 2 silver cubes Ex : 2 silver cubes

Rearranging Equations Density = mass / volume Rearranging Equations Density = mass / volume m D V D = m / Vm = D V V = m / D

Table: Density VariableEnglishSI VariableEnglishSI DensityD lb-masskg DensityD lb-masskg yd 3 m 3 yd 3 m 3 Massm lb-masskg Massm lb-masskg VolumeV yd 3 m 3 VolumeV yd 3 m 3

Density Ex: What is the density of an object that has a mass of 30 kg and a volume of 60 m 3 ? Density = mass / volume Density = mass / volume D = 30 kg / 60 m 3 D = 0.5 kg/ m 3

Volume A Rectangular Object A Rectangular Object Volume = length X width X height Volume = length X width X height m 3, ft 3 m 3, ft 3 Pressure Mathlab Pressure Mathlab

Water Density of water = 1 g / cm 3 Density of water = 1 g / cm 3 Water Weight Density = 62.4 lb / ft 3 Water Weight Density = 62.4 lb / ft 3 Hydrometer – an instrument that measures density Hydrometer – an instrument that measures density

Specific gravity = density of a substance / density of water = density of a substance / density of water There is no unit Ex: Density of lead is g/cm 3 Specific gravity of lead is Specific gravity of lead is 11.34

Table: Specific Gravity Table: Specific Gravity VariableEnglish SI VariableEnglish SI Specific gravityg sp none none Specific gravityg sp none none Density of aD s lb/ ft 3 g/cm 3 Density of aD s lb/ ft 3 g/cm 3 Substance Substance Density of waterD w lb/ ft 3 g/cm 3 Density of waterD w lb/ ft 3 g/cm 3

The Tale of Archimedes Problem: Did the goldsmith steal some of the gold that was to be used in the Crown?????

The King was sure some of his gold was stolen. If Archimedes did not discover the answer Archimedes would pay with his life. If Archimedes did not discover the answer Archimedes would pay with his life.

Buoyant Force This is an upward force on an object that’s equal to the weight of the fluid displaced determining whether an object sinks or floats This is an upward force on an object that’s equal to the weight of the fluid displaced determining whether an object sinks or floats

Density and Buoyancy If you are putting solids in water (1g/ml), if the density is: If you are putting solids in water (1g/ml), if the density is: 1 g/ml or less float 1 g/ml or less float 1 g/ml or more sink 1 g/ml or more sink Apply this pattern to other liquids Apply this pattern to other liquids Density/buoyancy Activity Density/buoyancy Activity Density/buoyancy Activity Density/buoyancy Activity Specific Gravity Mathlab Specific Gravity Mathlab

Pressure Pressure = Force / Area Pressure = Force / Area

AREA Area = length X width Area = length X width m 2, ft 2 m 2, ft 2

Table: Pressure VariableEnglishSI VariableEnglishSI Pressure P PsiN/ m 2 Force FlbN Area Ain 2 m 2

Pressure Example A woman has stiletto heels on she weighs 120 lb and the heel is 0.5 “ X 0.5”. How much pressure would the heal exert if all the woman’s weight is on one heel? Area= 0.5” X 0.5” = 0.25 in 2 P = F / A = 120 lb / 0.25 in 2 = 480 psi ( psi= lb/ in 2 ) = 480 psi ( psi= lb/ in 2 ) More than enough to puncture skin or the aluminum of an airplane

Pascal’s Principle A change in pressure at any point in a confined fluid is transmitted undiminished throughout the fluid ex: barometer A change in pressure at any point in a confined fluid is transmitted undiminished throughout the fluid ex: barometer

Total Pressure = gage pressure + atmospheric pressure atmospheric pressure- many units 30 inches of mercury OR 14.7 psi

Table: Total Pressure Variable English English Variable English English Total pressure P totpsi inches Gage pressure P g psi inches Atmospheric P atm14.7 psi 30 in Pressure

Total Pressure Example A car tire needs a gage pressure of 30psi. What would be the total pressure on the tire? Total pressure = gage pressure + atmospheric pressure Atm press= 14.7 psi Tot press= 30 psi psi = 44.7 psi

Fluid Height Pressure = water weight density X height This can be used for any substance as long as you know the weight density

Fluid Height variableEnglish SI Pressure Plb/ft 2 kg/m 2 Water wgt  w 62.4 lb/ft kg/m 3 Density Fluid height h ft m

Pressure in Tanks The tank with the greatest fluid height has the greatest pressure (figure 1.26 pg 42) The tank with the greatest fluid height has the greatest pressure (figure 1.26 pg 42) If two tanks have the same height but different diameter the pressure at the bottom is the same If two tanks have the same height but different diameter the pressure at the bottom is the same (figure 1.28 pg 43) Even if the tank funnels down to a small bottom surface, the pressure remains the same for the same depth of fluid Even if the tank funnels down to a small bottom surface, the pressure remains the same for the same depth of fluid

Pressure in Tanks

Fluid Height Example A water tower is 300 ft high. What should the water pressure gage read at the bottom of the tower? Pressure = water weight density X height Pressure = 62.4 lb/ft 3 X 300ft Pressure = 18,720 lb / ft 2