ME 262 BASIC FLUID MECHANICS Assistant Professor Neslihan Semerci Lecture 1

(Introduction to Fluid Mechanics, and , dimensions, dimensional homogeneity and units, unit systems, , compressibility, , specific weight and specific )

1. INTRODUCTION Fluid mechanics is the study of fluids and on them. Fluids : liquids,gases, and plasmas

FLUID MECHANICS

Fluid Dynamics Fluid Statistics The study of fluids in motion The study of fluids at rest

Both liquid and gases are classifed as fluids. Fluid engineering applications  breathing, blood flow, swimming pump, fans, turbine, airplane, ships, rivers, pipes, icebergs, filters, jets

Almost everything in this planet either is a fluid or moved within or near a fluid. The concept of fluid: From the point of view of fluid mechanics, all matter consists of only two states: fluid or solid Technical distinction lies with the reaction of the two to an applied shear or tangential stress. “A solid can resist a shear stress by a static deformation” “Any shear applied to a fluid, no matter how small, will result in movement of that fluid.” “A fluid moves and deforms continuously as long as the shear stress applied.”

MOLECULAR STRUCTURE OF SOLID: A solid has a regular arrangement of particles (atoms, ions or molecules). The particles are close together and cannot move around so the shape of a solid is fixed. MOLECULAR STRUCTURE OF LIQUID: A liquid has an arrangement of particles that are close together (like a solid) but the particles are free to move because the of attraction between the particles is weaker than it is in a solid. A liquid will flow to take the shape of its container. MOLECULAR STRUCTURE OF GASES: A gas has no order, its particles are arranged at random. The particles in a gas are so far apart that there is no force of attraction between them. A gas will fill the whole of its container. A gas is easily compressed.

2. WEIGHT AND MASS An understanding of fluid properties requires a careful distinction between mass and weight. Mass: Property of a body of fluid that is a measure of its inertia or resistance to a change in motion. It’s also a measure of the quantity of fluid. Mass does not change with the body’s position, movement or alteration of its shape unless material is added or removed. Weight: Gravitational force acting on a body mass. Force with which a body is attracted toward the by gravitation. mass, kg

퐹 = 푚. 푎 acceleration, m/s2

Force (N) 2 푊 = 푚. 푔 acceleration of gravity, m/s

Weight (N) mass, kg g = 9.81 m/s2 in SI system = 32.2 ft/s2 in U.S. Customary System

3. DIMENSIONS, DIMENSIONAL HOMOGENITY AND UNITS Primary dimensions: In fluid mechanics there are only four primary dimensions from which all other dimensions can be derived. These are mass, length, time and temperature. Qualitative: Identify the nature, or type, of the characteristics (such as length, time, stress, and velocity). Quantitative: Numerical measure of the characteristics (such as 10 meter). Primary dimensions: Length, temperature, time, mass

Secondary dimensions: Velocity, length/time, Area, ∀olume.

4. UNIT SYSTEMS English System (United States Customary System) (English Gravitational Unit System) (British Units) Metric SI (International System)

SI system English System Mass, kg Mass, Ibm Length, m Length, foot(m) Time, s Time, second(s)

Force in English System: Force is usually considered to be one of the primary dimensions. This is the source of confusion and error that necessitates the use of a dimensional constant (gc) in many formulas.

Force = (mass) (acceleration) = m.a In SI system, the force unit is Newton (N). One Newton is equal to the force needed to accelerate a mass of one kilogram one meter per second per second. In English system, the force unit is the -force (Ibf) and is defined as the force required to accelerate a mass of 32.174 (1 slug) at a rate of 1 ft/s2.

a=1 m/s2 m= 1 kg F= 1 N

a=1 ft/s2 m= 32.174 Ibm F= 1 Ibf

1 N= 1 kg.m/s2 1 Ibf= 32.174 Ibm.ft/s2

A force of 1 N is roughly equivalent to the weight of a small apple (m=102 g) whereas a force of 1 pound-force is roughly equivalent to the weight of 4 medium apples (mtotal=454 g). Another force a unit is commonly used in many European countries is the kg-f (kilogram-force which is the weight of 1 kg mass at sea-level.

Force (kg-force) = 1 kg. 9.807 m/s2 =9.807 N At sea level a mass of 1 kg weighs 9.807 N. A mass of 1 Ibm however weighs 1 Ibf. W=mg = 1 Ibm.32.22 ft/s2 = 1 Ibf 1 Ibm ≠ 1 Ibf

5. PRESSURE Pressure defined as the amount of force exerted on a unit area of a substance.

Force Pressure = = N/m2 Area of which the force is applied

F P = A Unit : N/m2 or Pascal (Pa) (Also frequently used is “bar”, where 1 bar = 105 Pa)

Two important principles about pressure (Pascal’s Principles)

 Pressure act uniformly in all directions on a small volume of a fluid.

 In a fluid confined by solid boundaries, pressure acts perpendicular to the boundary.

6. COMPRESSIBILITY : Change of volume (V) of a substance that is subjected to a change in pressure on it. Quantity used to measure : bulk modulus of elasticity or, simply, bulk modulus, E. −∆푃 퐸 = (∆푉)/푉 The units are same as those for the pressure. Liquids are very slightly compressible. It would take a large change in pressure to produce a small change in volume.

“ LIQUIDS IS CONSIDERED AS INCOMPRESSIBLE”

Example 1: Compute the change in pressure that must be applied to change its volume 1 %.

E = ∆P × [∆V/V] Water 316.000 psi =∆P × [0.01] E = 316 000 psi

∆P = 3160 psi

7. DENSITY, SPECIFIC WEIGHT AND SPECIFIC GRAVITY Density: Amount of mass per unit volume of substance 푚 푚푎푠푠 푘푔 휌 = = , 푉 푣표푙푢푚푒 푚3

Units are kilograms per cubic meter in SI system and slugs per cubic foot in the U.S. customary units.

Specific Weight: The amount of weight per unit volume of a substance 푊 푊푒𝑖푔ℎ푡 푁 S푝푒푐𝑖푓𝑖푐 푤푒𝑖푔ℎ푡 = = = 푉 푉표푙푢푚푒 푚3 The units for specific weight Newton per cubic meters (N/m3) in the SI system and pounds per cubic foot in the U.S. customary system. Specific gravity: Ratio of the density of a substance to the density of water at 40C. Ratio of the specific weight of a substance to the specific weight of the water at 40C. 훾푠 휌푠 s푔 (푠푝푒푐𝑖푓𝑖푐 푔푟푎푣𝑖푡푦) = = 훾푤 푎푡 4℃ 휌푤 푎푡 40퐶

At 4℃ ρwater =1000

Example 2: A load of 200 Ib is exerted on a piston confining an oil in a circular cylinder with an inside diameter 2.5 inches. Compute the pressure. F P = A π×(2.5)2 Area = = 4.91 in2 4 200 Ib P = = 40.7 Ib/in2 4.91 in2

Example3 :a) Calculate the weight of a reservoir of oil if it has a mass of 825 kg.

w = m × g

= 825 kg × 9.81 m/s2 = 8093 kg. m/s2(N) = 8093 N = 8.093 kN

b) If the reservoir has a volume of 0.917 m3. Find its density, specific weight and specific gravity =?

m 825 kg Density=ρ = = V 0.917 m3 w 8.093 kN Specific weight γ = = = 8.93 kN/m3 V 0.917 m3 3 ρoil γoil 900 kg/m Specific gravity s. g = = = kg = 0.9 ρwater at 4℃ γwater at 4℃ 1000 at 4℃ m3

Density of water at 20 ℃ → 998 kg/m3, at 4 ℃ → 1000 kg/m3

Example 4: Glycerine at 20 ℃ has a specific gravity of 1.26. ρglycerine = ? γglycerine = ?

ρglycerine s. g = γwater at 4 ℃

ρgly. 1.26 = ρ = 1260 kg/m3 1000 gly.

w mg 1260kg m kg γ = = = × (9.81 ) = 12360 =12.36 kN gly. ∀ ∀ m3 s2 m2s2

Example 5: A container has a 5 m3 volume capacity and 1500 N when empty and 47 000 N when filled with a liquid.

ρliquid = ? γliquid = ? (s. g)liquid = ?

weight of liquid = 47 000 – 1500 N =45 500 N

w = m × g

45 500 = m × (9.81 m/s2)

m = 4638.12 kg

m 46.38.12 kg ρ = = = 928 kg/m3 ∀ 5 m3

w mg kg γ = = = 928 × 9.81m/s3 = 9103 N/m3 ∀ ∀ m3

928 kg/m3 s. g = = 0.928 1000 at 4 ℃