2. 1 Fluid Mechanics Chapter 13

3. 2 Fluid Anything that can flow A liquid or a gas

4. 3 Density Mass per unit volume Where  (rho) is the density, m is mass, and V is volume A homogeneous material has the same density throughout The SI unit of density is the kg/m 3.

5. 4 Specific gravity Should be called relative density, but we are stuck with the traditional term The ratio of its density to the density of water.

6. 5 Pressure Pressure is force per unit area, expressed in Pascals (Pa). 1 Pa = 1 N/m 2

7. 6 Pressure changes Pressure increases with depth –Atmospheric pressure is greater at sea level than on top of a mountain –Water pressure is greater in deeper water When y 2 is greater, p 2 is less.

8. 7 Open containers The pressure at the surface is atmospheric pressure, or p 0. If we are at a depth, h, below the surface,

9. 8 Pascal’s Law If we increase the pressure at the surface, the pressure at any depth increases by the same amount. The pressure is transmitted throughout the fluid – if it has a uniform density – this is a fairly safe assumption for most liquids and for gases over small distances.

10. 9 Pascal’s Law Used in hydraulics to use a small force over a small area to exert a large force over a large area. –See page 304

11. 10 Gauge pressure If the pressure in your tire equals atmospheric pressure, the tire is flat. When your pressure gauge reads 32 psi, that means the pressure in the tire is 32 psi above the atmospheric pressure.

12. 11 Absolute pressure Total pressure Atmospheric pressure at sea level is 101.3 kPa or 14.7 psi. Also called 1 atm

13. 12 Example A residential hot water heating system has an expansion tank in the attic, 12 m above the boiler. If the tank is open to the atmosphere, what is the gauge pressure in the boiler? What is the absolute pressure? p g = 118 kPa, p a =219 kPa

14. 13 Open-tube manometer Measures the pressure in a container.

15. 14 Barometers Long glass tubes full of mercury used to measure atmospheric pressure. h

16. 15 Buoyancy When an object is less dense than water, it floats.

17. 16 Archimedes's principle When an object is completely or partially immersed in a fluid, the fluid exerts an upward force on the object equal to the weight of the fluid displaced by the object. We call this upward force the buoyant force.

18. 17 Weight of water displaced

19. 18 Example A cork has a density of 200 kg/m 3. Find the fraction of the volume of the cork that is submerged when the cork floats in water.

20. 19 Example continued

21. 20 Example An ore sample weighs 14.00 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 9.00 N. Find the total volume and the density of the sample.

22. 21 Example continued

23. 22 Example continued

24. 23 Example continued

25. 24 Fluid Flow An ideal fluid is incompressible and has no internal friction. We will only deal with laminar flow, which has a steady-state pattern. We will not deal with turbulent flow, which is chaotic.

26. 25 Continuity equation The mass of a moving fluid doesn’t change as it flows.

27. 26 Volume flow rate The rate at which volume crosses a section of the tube:

28. 27 Example Blood flows from an artery of radius 0.3 cm, where it’s speed is 10 cm/s into a region where the radius has been reduced to 0.2 cm. What is the speed of the blood in the narrower region? 22.5 cm/s

29. 28 Bernoulli’s Equation Relates pressure, flow speed, and height for flow of ideal fluids. Derived in book by applying the work energy theorem to a flowing fluid

30. 29 Bernoulli’s Equation Make sure that your units are consistent. –Always use pascals, kg/m 3, and m/s Always use either all absolute pressures or all gauge pressures.

31. 30 Example A large tank of water has a small hole a distance h below the water surface. Find the speed of the water as it flows from the tank. V b =sqrt(2gh)

32. 31 On your own Water enters a house through a pipe with an inside diameter of 2.0 cm at an absolute pressure of 4.0 x 10 5 Pa. A 1.0 cm diameter pipe leads to the second-floor bathroom 5.0 m above. When the flow speed at the inlet pipe is 1.5 m/s, find the pressure and volume flow rate in the bathroom. 3.3 x 10 5 Pa4.7 x 10 -4 m 3 /s