BTE 1013 ENGINEERING SCIENCES

1. BTE 1013 ENGINEERING SCIENCES 11. HYDRAULICS AND HYDROSTATIC NAZARIN B. NORDIN nazarin@icam.edu.my

2. What you will learn: • Pascal’s law • Incompressibility of fluids • Pressure, force ratio • Archimedes principle • Density and relative density

3. Introduction to fluids A fluid is a substance that can flow and conform to the boundaries of any container in which we put them. e.g. water, air, glass.

4. A fluid is any substance that can flow such as a liquid or a gas. Fluids don’t have well defined shapes. A fluid takes on any shape to fit a container. The study of fluids can be divided into two categories : hydrostatics and hydrodynamics or fluid dynamics.

5. Basic properties of fluids Density (mass per unit volume) - Pressure(force per unit area) -

6. Basic properties of fluids Pressure(force per unit area) - Notice that from definition, pressure may depend on direction. However, this is not the case for static fluids. (why?).

7. Basic properties of fluids Pressure(force per unit area) - Unit of pressure: 1 pascal (Pa) = 1 Newton per square meter. 1 atm. = 1.01 x 105 Pa

8. Fluids at rest Pressure increases when we go “deeper” into water – why?

9. Fluids at rest Pressure of a fluid in static equilibrium depends on depth only

10. Example Which one of the four container + fluid has highest pressure at depth h? How about if (d) is move up (down) by distance h?

11. Pascal’s Princple • A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of the container as a direct consequence of Newton’s Law.

12. Example: Hydraulic level • Applied force Fi change in pressure p=Fi/Ai=Fo/Ao. • Therefore output force is Fo=FiAo/Ai. • Therefore • Fo > Fi if Ao > Ai • How about work done?

13. Archimedes’ Principle • Buoyant force– upward force in liquid because of increasing pressure in liquid as one goes down below the surface. • (a) a hole in water. Notice that the hole is in static equilibrium if it is filled with water.

14. Archimedes’ Principle • (a) a hole in water. Notice that the hole is in static equilibrium if it is filled with water. • Therefore the upward force = mfg, mf = mass of displaced water.

15. Archimedes’ Principle • (b) The hole in water is replaced by a solid with the same shape. • Since nothing changes in water, therefore the upward force = mfg, mf = mass of displaced water = buoyant force

16. Archimedes’ Principle • (c) The solid in water is replaced by a piece of wood with mw < mf.. • In this case the wood float on the surface with Fb=mwg.

17. Archimedes’ Principle • When a body is fully or partially submerged in a fluid, a buoyant force Fb from the surrounding fluid acts on the body. The force is directed upward and has a magnitude equal to the weight mfg of the fluid that has been displaced by the body.

18. Archimedes’ Principle • Question: Imagine a large sphere of water floating in outer space. The sphere of water is formed under its own gravity. Is there any buoyant force if an object enters this sphere of fluid?

19. PRESSURE • Pressure is the quantity that is related to the force acting on the walls of the balloon and is defined as the normal force per unit area. • If F is the force perpendicular to the surface area A, the pressure P is therefore • The pressure at a point in a fluid depends on the depth. • Greater depths result in greater pressures

20. Pascal’s Law: For a confined fluid in a container, the change in pressure will be transmitted without loss to every point of the liquid and to the walls of the container Archimedes’ Principle: Any body that is completely or partially submerged in a fluid will experience an upthrust that is equal to the weight of the fluid displaced by the body

21. Fluids in Motion • An ideal fluid is one that (i) flows smoothly, (ii) is non-viscuous, (iii) is incompressible, (iv) is irrotational. • The path of steady flow can be visualized using streamlines. • Under steady-state flow conditions, for a given time interval, the volume of liquid flowing into the tube must equal the volume of liquid flowing out of a tube.This is known as the Continuity Equation.

22. Flowing liquids • The continuity equation – conservation of mass in a incompressible liquid flow. v = velocity of fluid flowing through area A in the tube

23. Example • What is the volume flow rate of water if Ao=1.2cm2, A=0.35cm2 and h=45mm.

24. Bernoulli’s Equation • Bernoulli’s Equation relates the elevation y, speed v and pressure P of a fluid at any point in a tube. • According to Bernoulli’s Equation: • However, Bernoulli’s Equation is not • applicable to viscous fluids .

25. Bernoulli’s Equation • Bernoulli’s Equation is a consequence of conservation of energy in steady flow.

26. Bernoulli’s Equation • Bernoulli’s Equation is a consequence of conservation of energy in steady flow.

27. Bernoulli’s Equation • Adding together, we obtain (Bernoulli’s Equation)

28. Example • What is the speed v of the water emerging from the hole? • Show that v2=2gh(same as free fall)

29. DENSITY • The density is an important factor that • determines the behaviour of a fluid. • The density of a fluid is defined as the • mass m per unit volume V: • The SI unit for the density is

31. THANK YOU