3 Fluid PrinciplesGlencoe 13.3

P = F/A P = ρgh Derive the relationship between these two

pressure equations. Verify both yield Pascals for units.

Pressure

Pascal’s Principle = Hydraulics

Force is multiplied as a ratio of piston areas.

Pressure is consistent throughout a fluid.

Liquids are dense and incompressible.

P1 = F1/A1 P2 = F2/A2 P1=P2 Therefore F2 = F1(A2/A1) Force is multiplied as a

ratio of piston areas. NOTE: Trade-off is the

distance pistons travel. The small piston has to move the greater distance, because work (energy) is conserved.

Pascal’s Principle

Image source: How Stuff Works –Hydraulics

Archimedes found that an object displaces its own volume of the fluid it is in. Another way of saying this is…

Fbuoy = weight of fluid displaced

The buoyant force affects the object’s weight. The apparent weight = weight – buoyant force

Archimedes Principle

A cube of aluminum (10E-3 m3) is submerged in water.

ρAl = 2.7E3 kg/m3

ρH2O = 1E3 kg/m3

What is the buoyant force? What is the apparent weight?

Sample Problem

A cube of aluminum (1E-3 m3) is submerged in water.

ρAl = 2.7E3 kg/m3

ρH2O = 1E3 kg/m3

What is the buoyant force? 9.8N What is the apparent weight? 2.7*9.8 –

9.8 = 16.7 N

Sample Problem

As the velocity of a fluid increases, the pressure exerted by that fluid decreases.

P1 + 1/2 ρ v12  + ρ gh1 = P2  + 1/2 ρ v2

2  + ρ gh2 

W1 + KE1 + PE1 = W2 + KE2 + PE2

Bernoulli’s Principle

Lift: To maintain equilibrium in a straight and level flight, pilots must monitor the aircraft's speed and pitch angle. Those variables along with other factors are used in a formula to determine an aircraft's lift.

Lift=(1/2)(air density)(velocity)(aircraft's wing area)(coefficent of lift)

Air density decreases with altitude. The coefficent of lift varies with the

aircraft's type of airfoil.

Bernoulli’s Principle

When fluid moves through constriction, velocity increases so same amount of mass can move through at same time.

A1v1 = A2v2 EQUATION OF CONTINUITY

See ThinkQuest animation: http://library.thinkquest.org/27948/bernoulli.html

Bernoulli’s Principle

Ideal fluids are continuous, incompressible (therefore, not gases) and have laminar (smooth) flow.

Real fluids are turbulent, experience friction, and have viscosity variation.

Ideal Fluids

Image source: answers.com