2 Fluids Fluids (Ch. 6) – substances that can flow (gases, liquids) Fluids conform with the boundaries of any container in which they are placedFluids lack orderly long-range arrangement of atoms and molecules they consist ofFluids can be compressible and incompressible
3 Density and pressure Density SI unit of density: kg/m3 Blaise Pascal( )Density and pressureDensitySI unit of density: kg/m3Pressure (cf. Ch. 12)SI unit of pressure: N/m2 = Pa (pascal)Pressure is a scalar – at a given point in a fluid the measured force is the same in all directionsFor a uniform force on a flat area
4 Atmospheric pressure Atmospheric pressure: P0 = 1.00 atm = x 105 Pa
5 Fluids at restFor a fluid at rest (static equilibrium) the pressure is called hydrostaticFor a horizontal-base cylindrical water sample in a container
6 Fluids at restThe hydrostatic pressure at a point in a fluid depends on the depth of that point but not on any horizontal dimension of the fluid or its containerDifference between an absolute pressure and an atmospheric pressure is called the gauge pressure
7 Chapter 14Problem 12The tank is filled with water 2.00 m deep. At the bottom of one sidewall is a rectangular hatch 1.00 m high and 2.00 m wide that is hinged at the top of the hatch. (a) Determine the force the water causes on the hatch. (b) Find the torque caused by the water about the hinges.
9 Pascal’s principlePascal’s principle: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its containerHydraulic leverWith a hydraulic lever, a given force applied over a given distance can be transformed to a greater force applied over a smaller distance
10 Archimedes’ principle of Syracuse( BCE)Archimedes’ principleBuoyant force:For imaginary void in a fluidp at the bottom > p at the topArchimedes’ principle: when a body is submerged in a fluid, a buoyant force from the surrounding fluid acts on the body. The force is directed upward and has a magnitude equal to the weight of the fluid that has been displaced by the body
11 Archimedes’ principle Sinking:Floating:Apparent weight:If the object is floating at the surface of a fluid, the magnitude of the buoyant force (equal to the weight of the fluid displaced by the body) is equal to the magnitude of the gravitational force on the body
12 Chapter 14Problem 28A spherical aluminum ball of mass 1.26 kg contains an empty spherical cavity that is concentric with the ball. The ball barely floats in water. Calculate (a) the outer radius of the ball and (b) the radius of the cavity.
13 Motion of ideal fluids Flow of an ideal fluid: Steady (laminar) – the velocity of the moving fluid at any fixed point does not change with time (either in magnitude or direction)Incompressible – density is constant and uniformNonviscous – the fluid experiences no drag forceIrrotational – in this flow the test body will not rotate about its center of mass
14 Equation of continuity Equation of continuity For a steady flow of an ideal fluid through a tube with varying cross-sectionEquation of continuity
15 Bernoulli’s equation For a steady flow of an ideal fluid: Daniel Bernoulli( )Bernoulli’s equationFor a steady flow of an ideal fluid:Kinetic energyGravitational potential energyInternal (“pressure”) energy
17 Chapter 14Problem 49A hypodermic syringe contains a medicine having the density of water. The barrel of the syringe has a cross-sectional area A = 2.50 × 10-5 m2, and the needle has a cross-sectional area a = 1.00 × 10-8 m2. In the absence of a force on the plunger, the pressure everywhere is 1 atm. A force F of magnitude 2.00 N acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needle’s tip.