Chapter 9. Solids and Fluids (c)

Transcription

1 Chapter 9 Solids and Fluids (c)

2 EXAMPLE A small swimming pool has an area of 0 square meters. A wooden 4000-kg statue of density 500 kg/m 3 is then floated on top of the pool. How far does the water rise? Note: Density of water = 000 kg/m 3

3 Solution Given: ρ wood /ρ H0 = 0.5, A = 0 m, M = 4000 kg Find: h h Level is the same as if 4000 kg of water were added = 4 m 3 Consider problem: A volume V = 4 m 3 of water is added to a swimming pool. What is h? h = V / A = 40 cm

4 . Three objects rest on bathroom scales at a lake bottom. Object is a lead brick of volume 0. m 3 Object is a gold brick of volume 0. m 3 Object 3 is a lead brick of volume 0. m 3 DATA: specific gravity of lead =.3 specific gravity of gold = 9.3 specific gravity of mercury = 3.6 Which statement is true? a) # and # have the same buoyant force b) # and # register the same weights on the scales c) # and #3 have the same buoyant force d) # and #3 register the same weights on the scales e) If the lake were filled with mercury, the scales would not change. Quiz. What is your section number?

5 Equation of Continuity What goes in must come out! M = mass density ρa x = ρav t Mass that passes a point in pipe during time t Eq.of Continuity ρ A v = ρ A v

6 Example Water flows through a 4.0 cm diameter pipe at 5 cm/s. The pipe then narrows downstream and has a diameter of of.0 cm. What is the velocity of the water through the smaller pipe? Eq.of Continuity ρ A v = ρ A v Solution A v v = = r r A v v = 4v = 0 cm/s

7 Laminar Flow and Turbulence Laminar or Streamline Flow: Fluid elements move along smooth paths that don t cross Friction in laminar flow is called viscosity Turbulent flow Irregular paths Sets in for high gradients (large velocities or small pipes)

8 Laminar Flow No turbulence Non-viscous Ideal Fluids No friction between fluid layers Incompressible Density is same everywhere

9 Bernoulli s Equation P + ρv + ρgy = constant Physical content: the sum of the pressure, kinetic energy per unit volume, and the potential energy per unit volume has the same value at all points along a streamline. How can we derive this?

10 Bernoulli s Equation: derivation Physical basis: Work-energy relation All together now: With We get:

11 Example: Venturi Meter A very large pipe carries water with a very slow velocity and empties into a small pipe with a high velocity. If P is 7000 Pa lower than P, what is the velocity of the water in the small pipe?

12 Solution Given: P = 7000 Pa, ρ = 000 kg/m 3 Find: v Basic formula P + ρgh + ρv = constant P = v P v + ρ P = ρ v = 3.74 m/s

13 Applications of Bernoulli s Equation Venturi meter Curve balls Airplanes Beach Ball Demo

14 Example Water drains out of the bottom of a cooler at 3 m/s, what is the depth of the water above the valve? Basic formula Solution a b P + ρgh + ρv P a = constant + ρ gha + ρva = Pb + ρghb + v h = = 45.9 cm g Compare water at top(a) of cooler with water leaving valve(b). ρv b

15 Viscosity Diffusion Osmosis Three Vocabulary Words

16 Viscosity F = η Av d Viscosity refers to friction between the layers Pressure drop required to force water through pipes (Poiselle s Law) At high enough velocity, turbulence sets in

17 Diffusion Molecules move from region of high concentration to region of low concentration Fick s Law: Mass C C Diffusion rate = = DA time L D = diffusion coefficient

18 Osmosis Osmosis is the movement of water through a boundary while denying passage to specific molecules, e.g. salts