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3 Fluid dynamics 2

# 3 Fluid dynamics 2 - A vacuum cleaner Does the vacuum suck...

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Unformatted text preview: A vacuum cleaner Does the vacuum suck the dust? Strictly speaking, the pump of the cleaner creates a reduced pressure inside it and the air and dust are driven into the hose by higher pressure of the atmosphere. A barometer Pressure of the air, P atm , drives mercury into the hollow tube. There is no air and no pressure inside the tube. ρ = 13600 kg/m 3 - density of mercury evacuated volume = − = gh P P atm top ρ gh P atm ρ = h Therefore P atm is balanced by hydrostatic pressure of the mercury. A manometer – pressure gauge Now there is a fluid (gas) under pressure in the reservoir. A manometer is measuring gauge pressure The difference between the pressure inside the reservoir, P res , and P atm is now balanced by hydrostatic pressure of the mercury. gh P P atm res ρ = − gh P P atm res ρ + = – gauge pressure – absolute pressure Archimede’s principle: The buoyant force on an object is equal to the weight of the fluid displaced by the object. Buoyant force Vg g m F w w p ρ = = The buoyant force is applied to the center of gravity of the fluid, which is the geometrical center of the submerged volume of the body. Equal Volumes Feel Equal Buoyant Forces Suppose you had equal sized balls of cork, aluminum and lead, with respective densities of 0.2 , 2.7 , and 11.3 times the density of water. If the volume of each is 10 cubic centimeters then their masses are 2 , 27 , and 113 gram. The gravitational forces they experience are 0.02 , 0.27 , and 1.1 N....
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3 Fluid dynamics 2 - A vacuum cleaner Does the vacuum suck...

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