Fluid Behavior

Pressure Pressure is the amount of force on a given area P=F/A Pressure (in pascals) = Force (newtons)/Area(meters 2 ) If the area decreases, the amount of pressure increases If a book is placed on a nail over your hand, it would create enough pressure at the nail point to puncture your hand.

Finding the force is easy – F=ma Force = mass(in kg)*acceleration(9.8m/s 2 ) So, using mass and area of an object, we can determine the force and then the pressure You Try It What is the force & pressure of a 4 kg book that is 22 cm X 15 cm?

Water is special Water has pressure in all directions!! A book only has pressure on the bottom, where gravity is pulling down. Since water is a fluid, its molecules can slide past each other, like a stack of marbles Like a stack of marbles, when you press down, the stack pushes down and outwards

This is why a cup with a hole in the bottom will leak – the water is pushed out the hole by the pressure The amount of pressure at a given depth in a fluid depends on two items The depth of the fluid at that point The weight density of the fluid

Say What?!? In other words, the total amount of the water above does not change the amount of pressure at a given depth!! The pressure at the bottom of a 10 cm cup is the same as the pressure 10 cm into the ocean!! The water directly above is what is creating the pressure – the extra water around does not have any impact!!

Density is a measure of how close material is. It is calculated by mass/volume Water has a density of 1g/1cm 3 Sea water has a density of 1.025g/1cm 3 Copper has a density of 8.92g/1cm 3 Lead has a density of 11.35g/1cm 3 Gasoline has a density of.67g/1cm 3

Weight Density Weight Density is a conversion of density to units of weight – newtons and m 3 Densities in kg/m 3 and N/m 3 Water = 1000kg/m 3 or 9800N/m 3 Sea Water = 1025kg/m 3 or 10045N/m 3 Copper = 8920kg/m 3 or 87416N/m 3

You Try It What is the pressure at a depth of 2 m in Lake Michigan? P=(9800N/m 3 )(2m) P=19600N/m 3 or pascals What is the pressure at a depth of 33 m in the ocean (100 ft)? P=(10045N/m 3 )(33m) P=331485N/m 3 or pascals Atmospheric pressure is pascals

Water pressure pushes in all directions In a cup, that is outwards and downwards In the ocean, that would also be “inwards” on anything floating or swimming below the surface The deeper you go, the more the pressure increases

Buoyancy If you have every lifted a large rock from the bottom of the lake, you notice that it “gets heavier” as it comes out of the water This is because all objects have buoyancy when in water

Buoyancy is the upward pressure exerted on an object by the surrounding water Wait!! Doesn’t the water about a submerged object push down??? Yup!! But the bottom of the object is lower in the water, so there is greater pressure pushing up than pushing down!!

How Much Buoyancy? The buoyancy of an object depends on the amount of water that is displaced by the object when put into water Displaced means the water is moved If a coffee cup if completely filled with water, and then a golf ball is carefully put into it, some of the water will overflow This water is displaced by the golf ball

Archimede’s Principle Archimede determined that the buoyant force acting on an object is equal to the weight of the water displaced Buoyant force, or buoyancy, does not depend on depth!! You Try It!! What is the weight of a 50 N cement block at the bottom of the lake if it displaced 20 N of water? 50N – 20N = 30N weight There is 20N of buoyant force canceling some of the weight

Will it Float!?! The relationship between the weight of an object and the buoyant force acting on it will determine if it sinks or floats If it weighs more than the buoyant force, it will sink If it weighs less than the buoyant force, it will float If they are the same, it will be neutrally buoyant – the same as scuba diver!!

Take me to the River? Do we have to test a material in water to determine if it will sink or float? NO!! Comparing the densities of the object and the fluid will determine if an object will sink or float!! Wood has a density of about.8g/cm 3, while gasoline has a density of.67g/cm 3. Wood is more dense, so it will sink in gasoline!!

Altering density? Fish, alligators, submarines, and scuba divers all change their densities to enable them to sink deeper, float upwards, or remain stable at a specific depth A scuba diver wears a BC (buoyancy compensator) that they put air into or let air out to change their density and, thus, float upwards, sink more, or remain stable at a specific depth

Concrete Boats??? Concrete is like a rock – it sinks!! But if concrete is shaped like a boat, it will float!! The deciding factor is the shape of the boat! A boat is designed to displace water. The more water displaced, the more buoyant force pushing it up!!

Archimedes Again? Archimedes said that the buoyant force is equal to the weight of the water displaced. Therefore, any object that floats will displace water equal to the object’s total weight! A 700 pound daysailor (small sailboat) must be designed to so that the complete boat would displace more than 700 pounds of water! If a powerboat will have a weight of 1500 pounds when full of people, it must be designed to have that much displacement, or it will sink!!

Pascal’s Principle Since fluids do not compress under pressure, any pressure put on a fluid is passed on to all of the fluid! This is what enables us to use a simple hydraulic jack and lift a car or a house!

Using this equal pressure throughout a fluid, and changing area, we can create a large amount of force to lift something! Remember P=F/A, so F=PA! You don’t have to push very hard, as long as there is a large area!

Rescue Equipment! The fire department has a set of air bags that they put under cars to help lift the cars The bags are somewhat large (up to 4 ftX4 ft), so it does not take a lot of air pressure to lift a car!