Hydrodynamics Pressure Pascal Bernouli continutity.pptx

Fluid mechanics

1. Physics Hydrodynamics Prepared by Omar M. Gharib OMG

2. Our Achievement: Hydrodynamics

3. Pressure is defined as a normal force exerted by an object per unit area . Units of pressure are N/m 2 , which is called a pascal (Pa). Since the unit Pa is too small for pressures encountered in practice, kilopascal (1kPa =10 3 Pa) and megapascal (1 MPa = 10 6 Pa) are commonly used. Other units include bar , atm, lbf /in 2 =psi= 6890 Pa , 1 mmHg = 133 Pa

4. No Particles => New State Particle Mass Velocity Position Fluid Density Velocity Field Pressure Viscosity Fluid Anything that can flow A liquid or a gas Ideal Fluid has constant density and it is incompressible so its flow in either steady or laminar. Incompressible means that the density of the fluid does not depend on the pressure, it can not be compressed.

5. Absolute, gage, and vacuum pressures Pressure in a fluid at rest is independent of the shape of the container. Pressure is the same at all points on a horizontal plane in a given fluid. Actual pressure at a give point is called the absolute pressure . Most pressure-measuring devices are calibrated to read zero in the atmosphere, and therefore indicate gage pressure , . Pressure below atmospheric pressure are called vacuum pressure ,  

6. The water in a tank is pressurized by air, and the pressure is measured by a multifluid manometer as shown in Fig. The tank is located on a mountain at an altitude of 1400 m where the atmospheric pressure is 85.6 kPa. Determine the air pressure in the tank if h1 is 0.1 m, h2 is 0.2 m, and h3 is0.35 m. Take the densities of water, oil, and mercury to be 1000 kg/m, 850 kg/m, and 13,600 kg/m, respectively.

7. Compare the pressures at points 1, 2, 3 and 4

8. Question: A diver dives 35 meters below the surface of the sea . Is it safe for him to hold his breath completely while an emergency ascent to the surface? Explain your answer .  

9. Pascal’s Law (principle), A consequence of the pressure in a fluid remaining constant in the horizontal direction is that the pressure applied to a confined fluid Increases the pressure throughout by the same amount.

10. Example: Pascal’s Law The mass of the car (shown) is 1200 kg, how much needed force to be applied at the small piston to left the car with constant speed. Assume that the diameter of the larger piston is three times that of the smaller one. Compare the work done on these two pistons.

11. Buoyancy: Archimedes Principle What Causes Buoyancy? Is it the Pressure!?

12. Archimedes’ principle: When an object is immersed in a fluid, the fluid exerts an upward force on the object equal to the weight of the fluid displaced by the object.

13. Example A wooden sphere with a diameter of d = 10 cm and density ρ = 0.9 g/cm 3 is held under water by a string. What is the tension in the string? Consider the density of water to be 1.00 g/cm 3 .

14. Example A wooden sphere with a diameter of d = 10 cm and density ρ = 2 g/cm 3 is held under water by a string. What is the tension in the string? Consider the density of water to be 1.00 g/cm 3 .

15. TYPES OF FLUID Ideal fluid : a fluid with no viscosity, no surface tension and is incompressible. Real fluid : A fluid that has viscosity, surface tension and is compressible. Compressible fluid : will reduce its volume in the presence of external pressure. Incompressible fluid : is a fluid that does not change the volume of the fluid due to external pressure.

16. The Equation of Continuity Volume flow rate (Q) is defined as the amount (volume) of fluid flow per time unit For incompressible fluid, the volume flow rate is the same at any point in the fluid or Equation above is called continuity equation which states that : “At any points in fluid, the rate of volume flow is constant. The speed of flow will be greater if it passes the smaller cross-sectional”  

17. The average velocity of water flow in a pipe with diameter 4 cm is 4 m/s. Calculate the amount of fluid flowing per second (Q) Example

18. If the rate of flow of the water that out from the pipe as shown in diagram below is 10 liter/s. Determine the speed of water in the large hole and in the small hole. R 1 = 20 cm R 2 = 10 cm Example

19. Example An ideal fluid flow through a pipe that has two difference cross-sectional area. The diameter of both area are 15 cm and 10 cm. If the fluid’s speed in the smaller area 9 m/s, Determine the speed of the fluid when it pass through the large area.

20. Bernoulli’s Equation

21. A water pipe having a 2.5 cm inside diameter carries water into the basement of a house at a speed of 0.9 m/s and a pressure of 170 kPa. If the pipe tapers to 1.2 cm and rises to the second floor 7.6 m above the input point. What are the speed and water pressure at the second floor ? Example

22. Example In the figure, , find and .  

23. The venturi meter

24. A venturi meter with the big section area 10 cm 2 and small section area 5 cm 2 is used to measure the velocity of water flow in a pipe. Calculate the velocity of water flow in the pipe If the height difference of water surface in the meter is 15 cm. Example

25. Venturi meter with manometer

26. The diagram shows is a venturi meter with has manometer. The rate of flow of water which flow through the venturi is 3,200 cm 3 /s. the cross section area 1 and area 2 each is 40 cm 2 and 16 cm 2 . The density of mercury in the manometer is 13.6 g/cm 3 a. what is the speed of the water at the area 1 and area 2 ? b. what is the difference of pressure between pipe 1 and pipe 2 c. what is the difference of mercury high at the manometer ? Example

27. Pitot Tube

28. When the air flows through a Pitot tube, the difference in height between mercury columns (13.6 g/cm 3 ) in the manometer is 2 cm. Determine the flow speed of air (1.29 kg/m 3 Example

29. نقيم: تقييم ذاتي