Fluids & Elasticity (Buoyancy & Fluid Dynamics) Knight: Chapter 15 Fluids & Elasticity (Buoyancy & Fluid Dynamics)

Archimedes’ principle The buoyant force is equal to the weight of the fluid displaced.

i.e.1: Weather balloon A 600-kg weather balloon is designed to lift a 4,000-kg package. What volume should the balloon have after being inflated with helium in order for the total load to be lifted? (The density of helium and air are, respectively, He= .179 kg/m3 , Air= 1.28 kg/m3 at standard temperature and pressure)

Quiz Question 1 Imagine holding two bricks under water. Brick A is just beneath the surface of the water, while Brick B is at a greater depth. The force needed to hold Brick B in place is larger than the same as smaller than the force required to hold Brick A in place.

i.e.2: Ice cube How much of the ice cube’s mass is below the surface of the water? (The density of liquid and solid water are, respectively, H20= 1,000 kg/m3 and ice= 917 kg/m3.) d L

Quiz Question 2 A tin can has a volume of 0.001 m3 and a mass of 0.1 kg. Approximately how many grams of lead shot can it carry without sinking in water: 100 900 980 1000 1100

Fluid dynamics Ideal-fluid model Incompressible ( = constant) Nonviscous (water, not syrup) Laminar flow (no turbulence )

Questions… Imagine the block in an ideal fluid… How does P1 compare with P2 ? How does 1 compare with 2 ? h1 F1 h2 P1 h P2 F2

Fluids dynamics… Consider fluid flowing down a cylindrical pipe… What is the “Flow Rate”? x A

Equation of Continuity (Volume/time)in = (Volume/time)out A1 A2 v1 v2

Quiz Question 3 A blood platelet drifts along with the flow of blood through an artery that is partially blocked by a stenosis. As the platelet is moving through the stenotic region, its speed (in the stenotic region) is: increased decreased unchanged

Bernoulli’s Equation Conservation of energy yields: velocity elevation pressure

Quiz Question 4 A blood platelet drifts along with the flow of blood through an artery that is partially blocked by a stenosis. As the platelet is moving through the stenotic region, the pressure (in the stenotic region) is: larger than smaller than the same as the non-stenotic region. v

Quiz Question 5 An ideal fluid is pumped steadily up a vertical pipe with a uniform cross-section. The difference in pressure between a point at the top and at the bottom: is the same as it would be if the fluid were motionless. is greater at higher flow rates than at lower flow rates. is less at higher flow rates than at lower flow rates. does not depend on the density of the fluid. is zero.

Venturi Tubes Venturi tubes measure gas speeds in environments as different as chemistry laboratories, wind tunnels, and jet engines. The gas-flow speed can be determined from the liquid height h.

Venturi Tubes Venturi tubes measure gas speeds in environments as different as chemistry laboratories, wind tunnels, and jet engines. The gas-flow speed can be determined from the liquid height h.