ME804306-2 Fluid Mechanics Chapter 1 Introduction Dr. Kamel Mohamed Guedri Mechanical Engineering Department, The College of Engineering and Islamic Architecture,

ME804306-2Fluid Mechanics

Chapter 1

Introduction

Dr. Kamel Mohamed Guedri

Mechanical Engineering Department,The College of Engineering and Islamic Architecture,

Umm Al-Qura University, Room H1091

Website: https://uqu.edu.sa/kmguedriEmail: [email protected]

1. INTRODUCTION

S ta tic s D yn am ics

R ig id B od ies(Th in g s th a t d o n o t ch an g e sh ap e)

D efo rm ab le B od ies(Th in g s th a t d o ch an g e sh ap e)

In com p ress ib le C om p ress ib le

F lu id s

M ech an ics

Branch of Mechanics

Physical Characteristics of Fluids

• Fluid mechanics is the science that deals with the action of forces on fluids.

. Fluid is a substance

• The particles of which easily move and change position

• That will continuously deform

• A fluid can be either gas or liquid.

• Solid molecules are arranged in a specific lattice formation and their movement is restricted.

• Liquid molecules can move with respect to each other when a shearing force is applied.

• The spacing of the molecules of gases is much wider than that of either solids or liquids and it is also variable.

Distinction Between Solids, Liquids & Gases

Flow Classification

The subject of Fluid Mechanics

• Hydrodynamics deal with the flow of fluid with no density change, hydraulics, the study of fluid force on bodies immersed in flowing liquids or in low speed gas flows.

• Gas Dynamics deals with fluids that undergo significant density change

• Turning on our kitchen faucets

• Flicking on a light switch

• Driving cars

• The flow of bloods through our veins

• Coastal cities discharge their waste

• Air pollution

• And so on so forth …

Significance of Fluid Mechanics

Trends in Fluid Mechanics

• The science of fluid mechanics is developing at a rapid rate.

2. OBJECTIVES

• Work with two types of units.

• Define the nature of a fluid.

• Show where fluid mechanics concepts are common with those of solid mechanics and indicate some fundamental areas of difference.

• Introduce viscosity and show what are Newtonian and non-Newtonian fluids

• Define the appropriate physical properties and show how these allow differentiation between solids and fluids as well as between liquids and gases.

3. UNIT SYSTEMS

• SI UNITS

In the SI system, the unit of force, the Newton, is derived unit. The meter,

second and kilogram are base units.

• U.S. CUSTOMORY

In the US Customary system, the unit of mass, the slug, is a derived unit.

The foot, second and pound are base unit.

•We will work with two unit systems in FLUID MECHANICS:

• International System (SI)

• U.S. Customary (USCS)

Basic Unit System & Units

Derived Units There are many derived units all obtained from combination of the above primary units. Those most used are shown in the table below:

The SI system consists of six primary units, from which all quantities may be described but in fluid mechanics we are generally only interested in the top four units from this table.

Derived Units

Table summarizes these unit systems.

SI System of Units

• The corresponding unit of force derived from Newton’s second law:

“ the force required to accelerate a kilogram at one meter per second per second is defined as the Newton (N)”

The acceleration due to gravity at the earth’s surface: 9.81 m/s2.

Thus, the weight of one kilogram at the earth’s surface:

W = m g

= (1) (9.81) kg m / s2

= 9.81 N

Traditional Units

• The system of units that preceded SI units in several countries is the so-called English system.

Length = foot (ft) = 30.48 cm

Mass = slug = 14.59 kg

The force required to accelerate a mass of one slug at one foot per second per second is one pound force (lbf).

The mass unit in the traditional system is the pound mass (lbm).

DIMENSIONAL HOMOGENEITY

• All theoretically derived equations are dimensionally homogeneous:

dimensions of the left side of the equation must be the same as those on the

right side.

* Some empirical formulas used in engineering practice are not dimensionally homogeneous

• All equations must use consistent units: each term must have the

same units. Answers will be incorrect if the units in the equation are

not consistent. Always chose the system of units prior to solving the

problem

4. FLUID PROPERTIES

Specific Weight

Mass Density

Viscosity

Vapor Pressure

Surface tension

Capillarity

Bulk Modules of Elasticity

Isothermal Conditions

Adiabatic or Isentropic Conditions

Pressure Disturbances

Every fluid has certain characteristics by which its physical conditions may be described.

We call such characteristics as the fluid properties.

Properties involving the Mass or Weight of the Fluid

Mass Density (or density),

The “mass per unit volume” is mass density. Hence it has units of kilograms per cubic meter.

- The mass density of water at 4 oC is 1000 kg/m3 while it is 1.20 kg/m3 for air at 20 oC at standard pressure.

Specific Gravity, SG

• The specific gravity is the ratio of density of a given fluid to the density of water at a standard reference temperature (4 oC). It is defined as specific gravity, SG.

• The specific gravity of mercury at 20 oC is

Example 1 - Use the Density to Identify the Material:

An unknown liquid substance has a mass of 18.5 g and occupies a volume of 23.4 ml. (milliliter).

The density can be calculated as

ρ = [(18.5 g) / (1000 g/kg)] / [(23.4 ml) / (1000 ml/l) (1000 l/m3)]

    = (18.5 10-3 kg) / (23.4 10-6 m3)

    = 790 (kg/m3)

Example 2 - Use Density to Calculate the Mass of a Volume

The density of titanium is 4507 kg/m3. Calculate the mass of 0.17 m3 titanium!

m = (0.17 m3) (4507 kg/m3)

    = 766.2 (kg)

Specific Weight, The gravitational force per unit volume of fluid, or simply “weight per unit volume”:

γ = ρ g        

where

γ = specific weight (N/m3, lb/ft3)ρ = density (kg/m3, slugs/ft3)g = acceleration of gravity (9.81 m/s2, 32.174 ft/s2) 

Example - Specific Weight Water

Specific weight for water at 4 oC is 62.4 lb/ft3 (9.81 kN/m3) in US units.

With a density of water 1000 kg/m3 - specific weight in SI units can be calculated as

γ = (1000 kg/m3) (9.81 m/s2)

  = 9810 (N/m3)

= 9.81 (kN/m3)

With a density of water 1.940 slugs/ft3 - specific weight in US units can be calculated as

γ = (1.940 slugs/ft3) (32.174 ft/s2)

  = 62.4 (lb/ft3)

5. NEWTONIAN AND NON-NEWTONIAN FLUIDSA fluid is defined as a material that can not support a stress or as a

material that is continuously deformed by the application of a stress.

Figure 1.1: A fluid element before deformation.

Figure 1.2: Fluid element after the application of a force acting tangentially on the top of the element.

Pressure

Pressure is defined as force divided by the area that the force acts over

and therefore has units of F/A . It can be a result of an applied force (for

example pumping) or hydrostatic (weight of a column of fluid). The total

pressure is the sum of the applied and hydrostatic pressure.

Pressure will be discussed in more detail in the next chapter.