Chapter 9Chapter 9Fluid MechanicsFluid Mechanics

FluidsFluids

““A nonsolid state of matter in which the A nonsolid state of matter in which the atoms or molecules are free to move past atoms or molecules are free to move past each other, as in a gas or liquid.” (p. 318) each other, as in a gas or liquid.” (p. 318)

Solids: definite shape and volume.Solids: definite shape and volume.

Liquids: definite volume but Liquids: definite volume but nono definite definite shape.shape.

Gases: no definite shape or volume; has Gases: no definite shape or volume; has volume and shape of container.volume and shape of container.

Mass DensityMass Density““The mass per unit volume of a substance.” (p. 319)The mass per unit volume of a substance.” (p. 319)Mass density = mass / volume Mass density = mass / volume

ρρ = m / V = m / V

For mass, we will use grams (g) or kilograms (kg) and for For mass, we will use grams (g) or kilograms (kg) and for volume we will use cmvolume we will use cm33, m, m33, liters (L) or milliliters (mL)., liters (L) or milliliters (mL).

1 m1 m33 = 1 x 10 = 1 x 1066 cm cm33

1 L = 1000 mL1 L = 1000 mL1 cm1 cm33 = 1 mL = 1 mL

Common units of density are g / cmCommon units of density are g / cm33, g / mL, and kg / m, g / mL, and kg / m33

Solids and liquids are almost Solids and liquids are almost incompressibleincompressible, which , which means their densities do not change. Gases are means their densities do not change. Gases are compressiblecompressible; so their densities depend on temperature ; so their densities depend on temperature and pressure.and pressure.

Buoyant ForceBuoyant Force

““A force that acts upward on an object A force that acts upward on an object submerged in a liquid or floating on a liquid’s submerged in a liquid or floating on a liquid’s surface.” (p. 319)surface.” (p. 319)Archimedes PrincipleArchimedes Principle: “any object submerged in : “any object submerged in a fluid experiences an upward buoyant force a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid equal in magnitude to the weight of the fluid displaced by the object.” (p. 320)displaced by the object.” (p. 320)Buoyant force = weight of displaced fluidBuoyant force = weight of displaced fluid

FFBB = F = Fgg (displaced fluid) = m (displaced fluid) = mf f g g (m(mff = mass of fluid = mass of fluid

displaced)displaced)

Other buoyancy formulas….Other buoyancy formulas….

An object submerged in a fluid has an “apparent An object submerged in a fluid has an “apparent weight” that is less then it’s normal weight: weight” that is less then it’s normal weight:

FFnetnet = F = FBB – F – Fgg (object) (object)

= = mmffg – mg – moog (mg (moo = mass of = mass of

submerged object)submerged object)

And since And since ρρ = m / V, m = = m / V, m = ρρV. V. So, the above So, the above formula becomesformula becomes

FFnetnet = = ρρffVVff g– g– ρρooVVoogg

Floating Objects Floating Objects

If an object floats, then its density is If an object floats, then its density is less thanless than the the density of the fluid (density of the fluid (ρρo o < < ρρff ) )For floating objects, the buoyant force equals the For floating objects, the buoyant force equals the weight of the floating object:weight of the floating object:

FFBB = F = Fgg (object) = m (object) = mooggThe density of an object determines the depth of The density of an object determines the depth of submersion:submersion:

FFnetnet = = ρρffVVff g– g– ρρooVVoog = 0g = 0 ρρffVVff – – ρρooVVo o = 0 = 0 (divide by g) (divide by g) ρρffVVff = = ρρooVVo o (add (add ρρooVVo o to both sides)to both sides)ρρff / / ρρoo = V = Voo / V / Vf f (divide by (divide by ρρooVVff))

Sinking Objects…Sinking Objects…

If an object sinks, then its density is If an object sinks, then its density is greater thangreater than the density of the fluid (the density of the fluid (ρρo o > > ρρff ). ).If an object sinks below the surface of a fluid, If an object sinks below the surface of a fluid, then the volume of the fluid displaced equals the then the volume of the fluid displaced equals the volume of the object. So, volume of the object. So, VVff = V = Voo and we can and we can replace both with just replace both with just V: V: FFnetnet = = ρρffVg– Vg– ρρooVg = Vg = FFBB – F – Fgg (object) (object)A simple relationship results from the above A simple relationship results from the above equation:equation:

FFgg (object) / F (object) / FB B = = ρρo o / / ρρff