L-14 Fluids [3] Fluids in Motion Fluid Dynamics Hydrodynamics Aerodynamics
Archimedes Principle F B W A buoyant force F B equal to the weight of displaced water is exerted on a submerged object.
Will it float? The object will float if the buoyant force is enough to support the object s weight The object will displace just enough water so that the buoyant force = its weight If it displaces as much water as possible and this does not match its weight, it will sink. Objects that have a density less than water will always float- when fully submerged, they weigh less than the water, so the water supports them
Floating objects lighter object heavier object too heavy The weight of displaced water is less than the weight of the object
Oil Tankers empty tanker full tanker
Floating in a cup of water Only a thin layer of water is needed for a ship to float in
Why does ice float? Water, the most plentiful substance on earth is also one of the most unusual in its behavior in that it expands when it freezes. Since it expands the density of ice is slightly less than the density of water (917 kg/ m 3 as compared to 1000 kg/ m 3 for water). That s why you about 90% of an iceberg is submerged.
Hot air balloon The ideal gas law tells is that when a gas is heated, its density goes down so the air density inside the balloon is less than the density of cold air on the outside. The cold air exerts an upward buoyant force on the balloon.
Fluid Flow The physics of fluid flow was worked out by Daniel Bernoulli He was born in Switzerland in 1700 He was one of 5 brothers and came from a large family of mathematicians and scientists.
Fluid flow can help us visualize the pressure in a liquid increasing pressure The outflow speed of the water is largest at the bottom because the pressure is greatest there.
How do we measure fluid flow? We see how much comes out in some time interval Time how long it takes to fill the bucket, say 30 seconds the flow rate is then 1 bucket say per 30 seconds in other words volume per unit time gallons per min (gpm), liters/s, cubic feet per min (cfm), gpf, or m 3 /s volume flow rate
Volume flow rate If the water comes out of a tube of cross sectional area A with a flow speed u the volume flow rate is volume flow rate = u A (m/s m 2 ) m 3 /s To measure u just see how long it takes to fill a gallon jug from a hose and measure the diameter of the hose.
Mass flow rate We could also measure how much mass comes out per unit time kg/s for example if you are using a fluid of density ρ coming out of a hose of cross sectional area A with speed v the mass flow rate is mass flow rate = ρ u A
What makes water flow? Stanton, IA gravity by placing the water up high the pressure at the bottom is high enough to supply water to all parts of town that are lower than the tower
Pressure differences P 2 P 1 a pressure difference must be established across the ends of the pipe to push the water along. P 2 must be greater than P 1 This pressure difference can be set up by a water pump.
Water does not disappear! If water goes in one end of a pipe it must come out the other end (if there are no leaks of course. Sounds obvious, but it has a number of interesting consequences! v 1, A 1 v 2, A 2 This applies to pipes that have constrictions also.
Continuity of flow since whatever goes in must come out we have that the incoming flow rate outgoing flow rate or v 1 A 1 = v 2 A 2 thus the fluid in the narrow part of the tube must flow FASTER that the fluid on the left. Cardiologists use this to determine if arteries might be clogged.
Other examples - the nozzle effect you use this principle whenever you hold your finger over the end of the hose to make the water spray farther.
An amazing thing about moving fluids The pressure in a moving fluid is less than the pressure in a fluid at rest! this is Bernoulli's principle. Where a fluid moves faster its pressure is lower, where it moves slower, its pressure is higher. As we will see, this is the principle that makes airplanes work.
The Venturi Meter
Bernoulli applies to household plumbing too! wind roof air vent When the wind is really blowing, watch the water level in the toilet go up and down sewer
Prairie dogs know how to use Bernoulli's principle
atomizers fine droplets of liquid (not atoms) are sprayed from this device using the Bernoulli effect