Physics Chapter 9: Fluid Mechanics

Fluids  Fluids  Definition - Materials that Flow  Liquids  Definite Volume  Non-Compressible  Gasses  No Definite Volume  Compressible

Fluids  Mass Density  Mass / Unit Volume  Symbol   (rho)  m = mass (kg)  V = volume (m 3 )

Fluids  Mass Density  Density of Water 4 0 C)  1.0 g/cm 3 = 1.0 g/cc = 1.0 g/mL  1.0L = 1x10 -3 m 3

Fluids  Mass Density  Density of Other Materials  Page 319  Table 9-1  Gasses  Liquids  Solids

Fluids  Archimedes’ Principle  Any Fluid Applies a Buoyant Force to an Object that is partially or Completely Immersed in it; The Magnitude of the Buoyant Force Equals the Weight of the Fluid that the Object Displaces.

Fluids  Archimedes’ Principle  Apparent Weight  The Weight of an Object You “Feel”  The Net Force Acting on a Submerged or Partially Submerged Object

Fluids  Archimedes’ Principle

Fluids  Archimedes’ Principle  If F g > F buoyant the Object Will Sink  If F g < F buoyant the Object Will Float  If F g = F buoyant the Object Will be Neutrally Buoyant

Fluids  Archimedes’ Principle  For a Floating Object the Buoyant Force is Equal to the Weight of the Object

Fluids  Archimedes’ Principle  Object Volume and Gravity are Constant

Fluids  Pressure  Force Acting Perpendicular to a Surface Divided by the Area of the Surface  Units – N/m 2 = Pascal (Pa)

Fluids  Pressure  Pascal  1Pa = 1N/m 2  Very Small Quantity  ATM  1.013x10 5 Pa = bar = lb/in 2

Fluids  Pascal’s Principle  Any Change in the Pressure Applied to a Completely Enclosed Fluid Is Transmitted Undiminished to All Parts of the Fluid and the Enclosing Walls.

Fluids  Pascal’s Principle

Fluids  Pressure and Depth  Fluid, at a Given Depth, has Pressure Applied to It by the Fluid Above It

Fluids  Pressure and Depth

Fluids  Pressure and Depth

Fluids  Pressure and Depth

Fluids  Pressure and Depth

Fluids  Pressure and Depth  Air is a Fluid  Atmospheric Pressure Works by the Same Principles

Fluids  Problem  Neutron stars consist only of neutrons and have very high densities. A typical mass and radius of a neutron star is 2.7x10 28 kg and 1.2x10 3 m. What is the density of this star?

Fluids  Solution  m = 2.7x10 28 kg  r = 1.2x10 3 m

Fluids  Problem  A paperweight weighs 6.9N in air, but when immersed in water weighs 4.3N. What is the volume of the paperweight?

Fluids  Solution  W = 6.9N  W apparent = 4.3N

Fluids  Problem  In a car lift the output plunger has a radius of 9.0cm. The weight of the plunger and the car is 21,600N. What is the gage pressure of the hydraulic oil used in operating the lift?

Fluids  Solution  F = 2.16x10 4 N  r = 9.0cm = 0.09m

Fluids  Problem  A dentist chair with a patient in it weighs 2100N. The output plunger of a hydraulic system begins to lift the chair when the dentist’s foot applies a force of 55N to the input piston. Neglect any height difference between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston?

Fluids  Solution  F 1 = 55N  F 2 = 2100N

Fluids  Problem  A spring (k=1600N/m) is attached to the input piston of a hydraulic chamber and a rock with a mass of 40.0kg rests on the output plunger. The piston and the plunger are nearly at the same height and each has negligible mass. By how much is the spring compressed from its unstrained position?

Fluids  Solution  k = 1.6x10 3 N/m  A 2 = 15cm 2  A 1 = 65cm 2  m r = 40.0kg

Fluids  Homework  Pages 343 – 344  Problems  8 (a, 6.3x10 3 kg/m 3 b, 9.2x10 2 kg/m 3 )  16 (1.9x10 4 N)  18 (14N Downward)  19 (a, 2.6x10 6 Pa b, 1.8x10 5 N)

Fluids  Fluids in Motion  Fluid Flow  Laminar Flow (Streamline Flow)  Constant Flow of Fluid Particles  All Particles have Same Velocity  Turbulent Flow  Velocity Changes with Time  Due to Obstructions or Openings

Fluids  Fluids in Motion  Fluid Flow  Turbulent Flow Eddy Currents Direction of Flow

Fluids  Fluids in Motion  Fluid Flow  Compressible  Gasses  Incompressible  Liquids  Some Gasses Under Specific Circumstances

Fluids  Fluids in Motion  Viscosity (Resistance to Flow)  Viscous  Inefficient Use of Energy  Non-viscous  Efficient Use of Energy

Fluids  Fluids in Motion  Fluid Flow  Ideal Fluid  Incompressible Fluid with Zero Viscosity

Fluids  Fluids in Motion  Equation of Continuity  Initial Flow Rate = Final Flow Rate

Fluids  Fluids in Motion  Equation of Continuity  Mass Flow Rate

Fluids  Fluids in Motion  Equation of Continuity  Mass Flow Rate  Assuming Same Density and Time

Fluids  Fluids in Motion

Fluids  Fluids in Motion  Bernoulli’s Principle  The Pressure in a Fluid Decreases as the Fluid’s Velocity Increases

Fluids  Bernoulli’s Equation  Pressure Drops with Decreased Area

Fluids  Bernoulli’s Equation  Pressure Drops with Increased Height

Fluids  Bernoulli’s Equation  In the steady flow of a nonviscous, incompressible fluid of density , the pressure P, the fluid speed v, and the elevation y at any two points are related.

Fluids  Bernoulli’s Equation For Static Fluids

Fluids  Bernoulli’s Equation  For Moving Fluids with No Change in Elevation

Fluids  Fluids in Motion

Fluids  Gasses  The Ideal Gas Law  Pressure  Volume  Number of Particles  Boltzmann’s Constant (k B ) = 1.38x J/K  Temperature (in Kelvin)

Fluids  Gasses  The Ideal Gas Law  If Number of Particles is Constant

Fluids  Problem  A dump truck traveling at 27m/s has its load covered by a tarp. By how much does the pressure inside the cargo area beneath the tarp exceed the outside pressure?

Fluids  Solution   air = 1.29kg/m 3  v 1 = 0m/s  v 2 = 27m/s

Fluids  Problem  Laura can fill a bucket from a water hose in 30.0s. If she covers up part of the hose’s opening with her thumb the velocity of the water doubles. How long will it take Laura to fill the bucket now?

Fluids  Solution  t 1 = 30.0s  v 2 = 2v 1

Fluids  Problem  The water supply of a building is fed through a main pipe that is 6.0cm in diameter. A 2.0cm diameter faucet tap is positioned 2.00m above the main pipe and can fill a 2.5x10 -2 m 3 container in 30.0s. What is the velocity that the water leaves the faucet?

Fluids  Solution  r 1 = 3.0cm  r 2 = 1.0cm  h 2 -h 1 = 2.00m   = 1000kg/m 3  t = 30.0s  V = 0.025m 3

Fluids  Problem  The water supply of a building is fed through a main pipe that is 6.0cm in diameter. A 2.0cm diameter faucet tap is positioned 2.00m above the main pipe and can fill a 2.5x10 -2 m 3 container in 30.0s. What is the gage pressure in the main pipe (difference in pressure)?

Fluids  Solution  r 1 = 3.0cm  r 2 = 1.0cm  h 2 -h 1 = 2.00m   = 1000kg/m 3  t = 30.0s  V = 0.025m 3  v 2 = 2.7m/s

Fluids  Problem  The pressure on an ideal gas is cut in half, resulting in a decrease in temperature to ¾ of the original value. What is the ratio of the final volume to the original volume of the gas?

Fluids  Solution  P 2 = ½ P 1  T 2 = ¾ T 1

Fluids  Homework  Page  Problems  24 (12.6m/s)  29 (474K)  30 (21.3K)