Archimedes, the Greek philosopher discovered the relationship between bouyancy or the tendency to float and displaced liquid when he climbed into his bathtub.

An immersed object is bouyed up by a force equal to the weight of the fluid it displaces. Bouyant force = weight of dicplaced fluid F bouyant = weight of dicsplaced fluid F = pgV

Bouyancy: Sink or Float? If the density of the block is more than the density of the water, the bouyant force is less than the weight and the block will sink Sink: d block > d water

If the density of the block is less than the density of the liquid, the bouyant force can equal the weight and the block will float. Float: d block < d water

Would a 10-cm 3 block with a density of 7.8 g/cm3 float in water? With the density of water (p water ) = 1.0 gm cm 3, just compare the densities. Since d block > d water, then the block will sink

Air Resistance If you drop a feather and a cannonball at the same time, from the same height, which will ht the ground first? The cannonball of course. The feather took longer to hit the floor because it has much more surface area bouncing against the air molecules. The air resistance slows it down.air resistance

Air resistance refers to a force that acts against relative motion of an object through a liquid or gas. It is also known as drag and acts in an opposite direction. It also directly depends on the velocity BACK

Fluids in motion often behave in complex and unpredictable ways. However, we can understand many aspects of fluid on the basis of a simple model that in many cases is reasonably realistic. The volume of liquid that flows through a pipe per unit time is easy to figure out. The rate of R of a liquid through the pipe is R = vtA/t = vA

The rate of flow is the product of the liquid speed and the cross sectional area. If the pipe size varies, the speed of a liquid also varies so as to keep R constant, so that v1A1 = v2A2 This is the equation of continuity

When a liquid is flowing in a pipe in a region where the pipe diameter gets smaller, its speed increases. A change in speed is acceleration, which means that a net force must be acting on the liquid. The liquid speed is also affected by changes in the height of the pipe. If the liquid rises, it slows down, and if the liquid falls, it speeds up. The relationship turns out to be, P 1 + pgh 1 + ½ p v 1 2 = P 2 + pgh 2 + ½ p v 2 2