Knight: Chapter 15

Fluids & Elasticity(Buoyancy & Fluid Dynamics)

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

Archimedes’ principle

i.e.1: Weather balloonA 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 1Imagine 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

1. larger than2. the same as3. smaller than the force required to hold Brick A in place.

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.)

i.e.2: Ice cube

dL

Quiz Question 2A 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:

1. 1002. 9003. 9804. 10005. 1100

Fluid dynamics

Ideal-fluid model

Incompressible ( = constant)

Nonviscous (water, not syrup)

Laminar flow (no turbulence )

Imagine the block in an ideal fluid…

How does P1 compare with P2 ?

How does 1 compare with 2 ? h1

h2

F1

F2

hP1

P2

Questions…

Consider fluid flowing down a cylindrical pipe…

What is the “Flow Rate”?

Fluids dynamics…

x

A

Equation of Continuity

(Volume/time)in = (Volume/time)out

A1

A2v1 v2

Quiz Question 3A 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:

1. increased2. decreased3. unchanged

Bernoulli’s Equation

pressure

elevation

velocity

Conservation of energy yields:

Quiz Question 4A 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:

1. larger than2. smaller than3. the same as

the non-stenotic region.

v

Quiz Question 5An 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:

1. is the same as it would be if the fluid were motionless.

2. is greater at higher flow rates than at lower flow rates.

3. is less at higher flow rates than at lower flow rates.

4. does not depend on the density of the fluid.5. 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.