FLUID MECHANICS

1. FLUID MECHANICS

2. FLUID MECHANICS • Fluid Mechanics is defined as physical science dealing with the action of fluids at rest or in motion, and applications of devices in engineering using fluids. • It is applicable in diverse fields such as aeronautics (Airplane; Aviation), chemical, civil and mechanical engineering, meteorology, naval architecture (Ships and Shipbuilding), and oceanography. • Fluid is any thing that can flow from one point to another (i.e.both liquids and gases) • The term hydrodynamics is applied to the flow of fluid which is considered to have incompressibility such as liquid and Aerodynamics is applied to the flow of fluid basing to the theory of flight, in which the fluid is considered to have compressibility effects such as gases.

3. FLUID MECHANICS • Fluid mechanics can be subdivided into two major areas, • Fluid statics, which deals with fluids at rest, and • Fluid dynamics, concerned with fluids in motion.

4. (i): FLUID STATICS • The key concepts/basic fluid properties to be discussed here, are • Density • Pressure • Viscosity a) Density (ρ) is the mass of a substance per unit volume Mathematically expressed: Density = mass/volume ρ = m/v The S.I unit of density is kg/m3 or 1g/cm3= 1000 kg/m3

5. FLUID STATICS cont… • For all practical purposes, liquids are considered to be incompressible, i.e., their volume and density are not affected by pressure. However, the effect of temperature on density of liquids cannot be ignored because liquids expand and contract when temperature changes. • Note: Both pressure and temperature affect density of gases. (P=mRT/v P= ρRT) • Specific Gravity (S.G) of the substance is the ratio of its density to the density of water at 4oC

6. FLUID STATICS cont… • APPLICATION OF DENSITY • To determine the charge condition of storage battery by measuring the density of its electrolytes( like H2SO4), as the battery discharge, H2SO4 combines with lead to form lead sulphate which is decreasing the concentration of solution hence decrease the density(densitometer) • To determine the quality of milk in dairy industry (Hydrometer)

7. FLUID STATICS cont… (b) Pressure (p)is the normal force acting per unit area Mathematically expressed: Pressure = Force/unit area • P = F/A • The S.I unit of pressure is Pa or N/m2 • 1Pa=1 N/m2 1atm =760mmHg= 1.013 x 105Pa 1bar= 105Pa 1mbar= 100Pa 1 kilopascal (kPa) = 1000Pa,

8. FLUID STATICS cont… • Pressure Scales • Since we live in an atmosphere of pressurised air, we have to decide on the datum, where the pressure would be zero. • There are 2 pressure scales; (i) Absolute scale: Readings taken on this scale are called absolute pressure and have suffix (a). • Absolute pressure is the total pressure in a fluid. (ii) Gauge scale: Readings made on this scale are called gauge pressure and have suffix (g) • Gauge pressure is the difference between absolute pressure and atmospheric pressure • The gauge scale is the most common scale used in the power plants. • Therefore, we use standard atmospheric pressure set at 101.3 kPa.

9. FLUID STATICS cont… • The correlation of the two scales is as follows: p (a) = p (g) + Standard Atmospheric pressure • where; p(a) is absolute pressure , p(g) is gauge pressure and standard atmospheric pressure is 101.3kPa (a) • APPLICATIONS OF PRESSURE SCALES • Blood pressure • Compressed gas tank • Car tires

10. FLUID STATICS cont… • EXAMPLE • If instrument air gauge pressure is 580-kPa (g), what is its absolute value? Soln p(a) = 580 kPa (g) + 101.3 kPa • Therefore the absolute gauge pressure is 681.3 kPa (a)

11. FLUID STATICS cont… • EXAMPLE • In an air-operated valve (AOV), the area of the actuator diaphragm is 0.1 m2. What minimum force must the spring exert on the diaphragm to counteract the force generated by the throttled instrument air at an absolute pressure of 200 kPa (a).

12. FLUID STATICS cont… • Soln p (a) = p (g) + Standard Atmospheric pressure p (g) = p (a) - Standard Atmospheric pressure p(g) = 200 kPa (a) -101.3 kPa = 98.7 kPa (g) = 98.7 x 103Pa (g) Hence, the force produced by this pressure differential: = p (g) x A = 98.7 x 103Pa (g) x 0.1m2 = 9.87 x 103N Therefore minimum force must the spring exert on the diaphragm is 9.87 x 103N

13. FLUID STATICS cont… • Pascal’s Law • Pascal’s law states that: The pressure on a fluid is equal in all directions and in all parts of the container. • As liquid flows into the large container at the bottom of this illustration, pressure pushes the liquid equally up into the tubes above the container. The liquid rises to the same level in all of the tubes, reguardless of the shape or angle of the tube.

14. FLUID STATICS cont… .

15. FLUID STATICS cont… • A piston with small cross-sectional area A1 exerts a force F1 on the surface of a liquid such as oil. The applied pressure is transmitted through the connecting pipe to a larger piston of area A2. • P = F1/A1 • The applied pressure P is the same in both cylinders. • P = F1/A1 = F2/A2

16. FLUID STATICS cont… • EXAMPLE • Calculate the force of larger piston pushed up if the force of smaller piston is 25N in hydraulic press with the surface area of 400cm2 and 250cm2 respectively.

17. FLUID STATICS cont… • APPLICATIONS OF PRESSURE IN GENERAL • Car lifts • Car jacks • Hydraulic brakes • Factors Affecting Pressure of Fluids The factors affecting the static liquid pressure are: • Pressure of the gas or vapour above the liquid (p) • Height (h) of the liquid column/head above the point, • Density (ρ) of the liquid, and • Gravitational acceleration (g). Mathematically expressed: • Ps = Pgas + h ρ g

18. FLUID STATICS cont… • The factors affecting the gas pressure are: • Mass of Gas (m); • Absolute temperature (T) explained in the Thermodynamics course; • Tank volume (V), and • Gas constant (R) specific to a given gas. • Mathematically expressed: • P = mRT/v P = ρRT(This equation is called the Ideal Gas Law)