Introduction ToIntroduction To

FluidsFluids

DensityDensity = m/V= m/V: density (kg/m: density (kg/m33))m: mass (kg)m: mass (kg)V: volume (mV: volume (m33))

PressurePressurep = F/Ap = F/Ap : pressure (Pa)p : pressure (Pa)F: force (N)F: force (N)A: area (mA: area (m22))

PressurePressureThe pressure of a fluid is exerted in all directions.The force on a surface caused by pressure is always normal to the surface.

The Pressure of a LiquidThe Pressure of a Liquidp = p = ghgh

p: pressure (Pa)p: pressure (Pa): density (kg/m3): density (kg/m3)g: acceleration constant (9.8 m/sg: acceleration constant (9.8 m/s22))h: height of liquid column (m)h: height of liquid column (m)

Absolute PressureAbsolute Pressurep = pp = poo + + ghgh

p: pressure (Pa)p: pressure (Pa)ppoo: atmospheric pressure (Pa): atmospheric pressure (Pa)

gh: liquid pressure (Pa)gh: liquid pressure (Pa)

Piston

Density of Hg13,400 kg/m2

ProblemProblem

25 cm

A

Area of piston: 8 cm2

Weight of piston: 200 N

What is total pressure at point A?

Floating is a type of equilibriumFloating is a type of equilibrium

Floating is a type of Floating is a type of equilibriumequilibrium

Archimedes’ Principle: Archimedes’ Principle: a body a body immersed in a fluid is buoyed up immersed in a fluid is buoyed up by a force that is equal to the by a force that is equal to the weight of the fluid displaced.weight of the fluid displaced.

Buoyant Force: the upward Buoyant Force: the upward force exerted on a submerged force exerted on a submerged or partially submerged body.or partially submerged body.

Calculating Buoyant ForceCalculating Buoyant Force

FFbuoybuoy = = VgVg

FFbuoybuoy: the buoyant force exerted on : the buoyant force exerted on a submerged or partially a submerged or partially submerged object.submerged object.

V: the volume of displaced liquid.V: the volume of displaced liquid.: the density of the displaced : the density of the displaced

liquid.liquid.

Buoyant force on submerged Buoyant force on submerged objectobject

mg

Fbuoy = Vg

Note: if Fbuoy < mg, the object will sink deeper!

Buoyant force on submerged Buoyant force on submerged objectobject

mg

Fbuoy = Vg

SCUBA divers use a buoyancy control system to maintain

neutral buoyancy (equilibrium!)

Buoyant force on floating objectBuoyant force on floating object

mg

Fbuoy = Vg

If the object floats, we know for a fact Fbuoy = mg!

Fluid Flow ContinuityFluid Flow ContinuityConservation of Mass results Conservation of Mass results

in continuity of fluid flow.in continuity of fluid flow.The volume per unit time of The volume per unit time of

water flowing in a pipe is water flowing in a pipe is constant throughout the pipe.constant throughout the pipe.

Fluid Flow ContinuityFluid Flow ContinuityAA11vv11 = A = A22vv22

–AA11, A, A22: cross sectional : cross sectional areas at points 1 and 2areas at points 1 and 2

–vv11, v, v22: speed of fluid flow : speed of fluid flow at points 1 and 2at points 1 and 2

Fluid Flow ContinuityFluid Flow ContinuityV = AvtV = Avt

–V: volume of fluid (mV: volume of fluid (m33))–A: cross sectional areas at a point A: cross sectional areas at a point

in the pipe (min the pipe (m22))–vv: : speed of fluid flow at a point in speed of fluid flow at a point in

the pipe (m/s)the pipe (m/s)–t: time (s)t: time (s)

AnnouncementsAnnouncements 04/19/2304/19/23

• Lunch Bunch pretest due tomorrow Lunch Bunch pretest due tomorrow at beginning of regular class.at beginning of regular class.

• Engineering seminar Engineering seminar announcement.announcement.

Bernoulli’s TheoremBernoulli’s TheoremThe sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous incompressible fluid in streamline flow.

Bernoulli’s TheoremBernoulli’s Theorem

All other considerations being equal, when fluid moves faster, the pressure drops.

Bernoulli’s TheoremBernoulli’s Theorem p + p + g h + ½ g h + ½ vv22 = Constant = Constant

– p : pressure (Pa)p : pressure (Pa) : density of fluid (kg/m: density of fluid (kg/m33))– g: gravitational acceleration constant (9.8 g: gravitational acceleration constant (9.8

m/sm/s22))– h: height above lowest point (m)h: height above lowest point (m)– v: v: speed of fluid flow at a point in the pipe speed of fluid flow at a point in the pipe

(m/s)(m/s)

Bernoulli’s TheoremBernoulli’s Theorem

pp11 + + g h g h11 + ½ + ½ vv1122 = p = p22

+ + g h g h22 + ½ + ½ vv2222