Buoyancy Pressure Physics of Fluids Buoyant Force the

Buoyancy & Pressure Physics of Fluids

Buoyant Force the upward force applied on an object by a fluid

Archimedes Principle • An object immersed in a fluid has an upward (buoyant) force equal to the weight of the fluid it displaces. FB = buoyant force mfd = mass of fluid displaced g = acceleration due to gravity (9. 81 m/s 2)

Archimedes Principle So…how exactly does one measure the mass of the fluid displaced? You could use an overflow can. Fill a container with water (or other fluid) and as the object is submerged the water displaced will overflow into another container…then you could measure the mass.

Archimedes Principle Ok…But how would that work for this? Overflow can and a balance to measure mass? There must be another way!

Archimedes Principle We know how to find volume of an object by fluid displacement right? Can we use the volume of the object that is submerged to find the mass of the fluid displaced? We learned in Chemistry how to find volume by displacement, so… How does this help us? Is there some kind of relationship between mass and volume?

Archimedes Principle Of course there is… Density!! The symbol for density is the greek letter “rho” Ok… We need mass so… Let’s solve this equation for mass. ρ

Archimedes Principle Let’s combine these ideas to get a usable equation for finding buoyant force (FB ). So…. Starting with… Then substituting the density relationship solved for mass

Apparent Weight • defined as the weight we “feel” • it is a force, so measured in Newtons (N) • when you are standing on a surface, apparent weight is measured by the normal force • When an object is suspended, apparent weight is measured by the tension. In air, both of these scales measure the “apparent weight” which is also just the “weight” of the object in that environment. FN = scale reading scale 0 Fg T = scale reading 0 Fg

Apparent Weight When objects are submerged in a fluid, they experience the upward buoyant force, so the apparent weight is less than the actual force of gravity “weight”. How much less? . . . An amount equal to the buoyant force. Submerged in a pool FB = Buoyant force T = scale reading FN = scale reading Fg scale Fg So, apparent weight is 0 0 So, apparent weight is

Conditions for an object to Float • apparent weight = 0, • the weight of the object = weight of the fluid displaced (or buoyant force). • Fg= FB = ρVg • Vfd = Vsubmerged • object density < fluid density

Conditions for an object to sink • The object can’t displace enough fluid weight to equal its own weight. • Fg > FB • Object density > fluid density • Vfd = Vobject • Apparent Weight = Fg - FB FB = buoyant force = f. Vfdg

Conditions for Neutral Buoyancy • apparent weight = 0 • the weight of the object = weight of the fluid displaced (or buoyant force). • Fg= FB – but only when the object is completely submerged. • Vfd = Vsubmerged • object density = fluid density

Mass density vs Weight Density Are you aware there are different kinds of densities? • Mass Density (ρ) • Weight Density (ρw) – Ratio between mass and volume – Ratio between weight and volume – values for fresh water To sum up: weight density already has “g” multiplied into it

Pressure defined as force per unit area • Units: Pa (N/m 2), lb/in 2, atm, torr, mm. Hg

Fluid Pressure • Fluid pressure is the force per unit area acting on the surface of any object in contact with that fluid. • Pressure is applied in a direction that is perpendicular to the surface of the object at the point of application. Note that the pressure pushing up on the bottom of the object is greater than the pressure pushing down on the top of the object. This difference is what causes buoyant force.

What does pressure do for us? • Pressure controls motion – Objects move from high pressure to low pressure…that is why the wind blows! • Pressure allows a suction cup to work – Air pressure pushes down on the top and is nearly zero on the bottom, so the suction cup sticks • Pressure is why a straw works – We lower the pressure inside the straw so that the air pressure pushing down on liquid outside the straw is forced up through the straw.

Atmospheric Pressure • defined as the pressure applied to any object due to the surrounding air. • equal to the weight of the molecules above the object pressing down Imagine an air column rising above you to the top of the atmosphere. All of those air molecules have weight and they are all pressing down on you. This is atmospheric pressure. At the bottom of the column the pressure is 1 atm.

What does “ 1 Atmosphere” of Pressure mean? We live at the bottom of an ocean of air known as the “atmosphere”. 1 atmosphere is the same pressure as a 760 mm tall column of Mercury will exert on a surface at its base. 1 atm is the same as 101, 300 Newtons per square meter or Pascals of pressure. (1 N/m 2 = 1 Pascal) This means each square meter of ground at sea level has 101, 300 N (22, 700 lbs) of force pushing down on it. How much force is pushing on you?

Atmospheric Pressure – some common units 1 atm is equal to … • 760 mm Hg • 101. 3 k. Pa • 760 torr • 14. 7 psi (lbs/in 2) • 1. 013 bar

Ok, so that is at sea level… What happens when you go up in a plane or under water? Your ears pop! But why? The pressure between the outside surface of your eardrum and the inside surface of your ear drum becomes different. That “popping” sound is the pressure equalizing itself.

Why does the pressure become different? • The pressure acting on an object changes with the object’s depth in the fluid. • As an object goes deeper, there are molecules of the fluid above it resulting in more weight pressing down, so higher pressure. Therefore, a person diving under water will experience more pressure on the outside of their eardrum than inside. And, a person going up in an airplane will experience less pressure on the outside of their eardrum than outside.

Pressure vs Depth We know that the pressure at any given depth in a fluid comes from the weight of the molecules above. That weight depends on a few factors…. • Density of the fluid (ρ) • Depth of object in the fluid (h) • The gravitational constant (g) So we can say…the change in pressure due to a fluid is directly proportional to the change in depth within that fluid. And we can calculate the change in pressure with…

Pressure vs Depth • Pressure increases in a fluid with depth • The shape of the container has no effect on pressure. Only Depth! The pressure at the bottom of the each is the same. This is why a dam must be built thicker at the bottom. Pressure is greater at the bottom due to depth, but has absolutely nothing to do with how large the body of water behind it is.

Pascal’s Principle Any external pressure applied to an enclosed non-compressible fluid is transmitted throughout that fluid unchanged in all directions.

Pascal’s Principle Pressure is transmitted UNCHANGED throughout the fluid, so… If the area is doubled, the force acting on that area will double! Pascal’s Principle is the underlying idea behind hydraulic devices.

Hydraulic Devices • Have a small piston and a large piston connected by a chamber filled with non -compressible (hydraulic) fluid. • Examples of these devices include: – A lift in an auto repair shop – A dumptruck – Landing gear on a plane – A backhoe – Trash compactors – The brake system on your car

Bernouilli’s Principle • The pressure in a moving stream of fluid is less than the pressure in the surrounding fluid. • As the velocity of a fluid increases, the pressure exerted by that fluid decreases. Example: Airplane wing. The air moves across the top of the wing faster so the pressure is less on the top surface than the bottom resulting in an upward net force.

Applications of Bernoulli’s Principle • Lift on an airplane wing – see previous slide • Spoilers on a race car – upside down airplane wing causes a downward force on car giving better traction. • Shower curtain creepingrunning water inside the shower curtain causes pressure to drop.