Chapter 11 Fluids

Defining a Fluid Ability to flow Difference between gas and liquid Gas or liquid Difference between gas and liquid Liquid has a definite volume

Mass Density Mass per unit volume Symbol => r Units => kg/m3 Specific Gravity Ratio of density of a substance to the density of water at 4° C Density of water is 1000 kg/m3 at 4°C

Pressure Force per unit area Units => N/m2 = pascal(Pa) psi 1 bar = 105 Pa

Atmospheric Pressure Caused by the weight of air above Extremely large pressure 1 atm = 1.013×105 Pa Exerted in all directions Barometers measure pressure

Pressure and Depth Fluid pressure increases with depth

Pressure and Depth Gauge pressure is only pressure relative to the atmospheric pressure Absolute or Total pressure must include the pressure of the atmosphere

Example Problem How much pressure would a submarine have to withstand at a depth of 5 km in the ocean? ( of sea water=1.025* 103kg/m3)

Example Problem

Example Problem

Pascal’s Principle Applied pressure to a fluid in a closed container is transmitted equally throughout the fluid Example: Hydraulic lifts

Archimede’s Principle FB A Buoyant Force that acts upward on an object submerged in or floating on a liquid Fg Apparent weight of the object will be less

Archimede’s Principle

Archimede’s Principle

Archimedes' Principle A buoyant force is equal to the weight of the fluid displaced FB Fg

Floating Object FB Net force is zero on floating object Fg

Archimedes' Principle Submerged object FB Fg

Archimede’s Principle Objects will float if the density of the object is less than or equal to the density of the liquid

Example Problem A piece of metal weighs 100.0 N in the air and 68 N in water. What is the density of the metal? (Density of water=1.00*103kg/m3)

Example Problem

Example Problem

Fluids in Motion Steady vs Unsteady Flow Steady flow Unsteady flow Velocity of particles at any point is constant Velocity at another point may be different, but still constant for that point River—Faster in the center and slower on the edges Unsteady flow Velocity of particles at a point continually changes Turbulent flow-an extreme case of unsteady flow River Rapids

Fluid in Motion Compressible vs Incompressible Incompressible Density of fluid is constant Liquids Compressible Gases are highly compressible

Fluid in Motion Viscous vs Nonviscous Viscous Does not flow readily One layer hinders other layers from flowing freely Honey-High Viscosity Water-Low viscosity No real fluid is nonviscous

Ideal Fluid Incompressible Non-viscous Non-turbulent—would form nice straight constant streamlines

Equation of Continuity Mass flow rate mass of fluid per second that flows through a tube Kg/s

Equation of Continuity Mass flow rate is constant for any given section of pipe What enters at one end of the pipe, must exit the other side of the pipe Thus, fluids will flow faster if size of tube gets smaller. Incompressible fluid Density is constant Called the volume flow rate

Example Problem Water flows through a 4.1 m diameter tunnel at a speed of 3.0 m/s. It then enters a 2.7m tunnel at the same level where the pressure is 82 kPa. Find the velocity of the water in the small tunnel.

Example Problem

Bernoulli’s Equation Pressure in a fluid is inversely proportional to fluid velocity Explains unbalanced force in acceleration of fluids Lift in planes As a fluid raises its elevation, the pressure decreases because of less fluid above it

Principle’s of Fluid Flow Bernoulli’s Equation Conservation of energy in fluids Work-energy theorom Uses energy per unit volume

Example Problem A large storage tank, open at the top, develops a hole 5 m below the surface of the water. What is the velocity of the water when it leaves the hole?

Example Problem

Example Problem

Example Problem Water flows through a 4.1 m diameter tunnel at a speed of 3.0 m/s. It then enters a 2.7m tunnel at the same level where the pressure is 82 kPa. Find the pressure in the wide portion of the tunnel.

Viscous Flow Fluid Flow is hindered by viscosity A fluid is visualized as thin layers Slowest at a boundary Fastest at the center Called Laminar flow A force is required to keep offset the forces from neighboring layers

Viscous Flow Force required to move any layer depends on Area of contact(A) Velocity of layer(v) Distance from immobile surface(y) Coefficient of viscocity (η)—Units are Pas

Viscous Flow This force is caused by a difference in pressure between two points in a pipe for viscous flow Flow rate depends on Pressure difference Radius of pipe Length of pipe Viscosity of fluid