1. 3 Fluid Principles Glencoe 13.3

2. P = F/A P = ρgh Derive the relationship between these two pressure equations. Verify both yield Pascals for units. Pressure

3. Pascal’s Principle = Hydraulics Force is multiplied as a ratio of piston areas.

4. 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

5. 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

6. 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

7. 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

8. As the velocity of a fluid increases, the pressure exerted by that fluid decreases. P1 + 1/2 ρ v12 + ρgh1= P2 + 1/2 ρ v22 + ρ gh2 W1 + KE1 + PE1 = W2+ KE2+ PE2 Bernoulli’s Principle

9. 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

10. 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

11. 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