FLUID MECHANICS (TPE 4106/3/W) Departement of Agricultural EngineeringUniversity of Brawijaya MalangReferention : Fluid Mechanics

CONTENTS

NumberSubjectsWeekCHAPTER 01INTRODUCTION01& 02CHAPTER 02DIMENSIONAL ANALYSIS03CHAPTER 03FLUID STATIC04 & 05CHAPTER 04FUNDAMENTALS OF FLUID FLOW06 & 07 CHAPTER 05FLUID FLOW IN PIPES07 & 08CHAPTER 06FLUID FLOW IN OPEN CHANNEL09 & 10

CHAPTER 07EQUIVALENT, COMPOUND, LOOPING AND BRANCHING PIPES10 & 12

Apa itu Fluida?Adalah sunstansi yang :mampu mengalir dan memenuhi (sesuai) bentuk wadahnya. Ketika dalam kesetimbangan tidak dapat menopang gaya tangensia dan gaya geser.mempunyai derajat kompresibilitas dan memberikan resistansi kecil pada perubahan bentuk.Dapat dalam ujud cair atau gas.Perbedaan antara cair dan gas :Cairan secara praktis inkompresibel sedangkan gas kompresibelCairan menempati volume yang pasti dan mempunyai permukaan bebas sedangkan massa gas berkembang sampai menempati bagian wadah yang memuatnya.

UNITSMassa

Panjang

WaktuKg

M

dtkThe unit for force in this system, the Newton, is derived from the units of mass and acceleration. From Newtons second law.Force in newtons = mass in kilogram x acceleration in m/s2orA force in 1 newton accelerations a mass of 1 kilogram at the rate 1 m/s2.

Newtons law of viscosity Figure 1.1 Deformation resulting from application of constant shear force

Newtonian or non-Newtonian Fluid Figure 1.2 Rheological diagram

ContinuumBerkenaan dengan hubungan aliran fluida dengan dasar matematik atau analitik, struktur molekul aktual aliran fluida dianggap sebagai medium kontinus hipotetik (hypothetical continuous medium), disebut continuum. Sebagai contoh, kecepatan pada sebuah titik dalam ruang tak tentu dalam suatu medium molekular, seharusnya nol pada semua waktu kecuali bila sebuah molekul menempati titik pasti ini, dan merupakan kecepatan molekul itu dan bukan kecepatan massa rata-rata partikel dalam kelompoktetanggaan. This dilemma is avoided if one considers velocity at a point to be the average or mass velocity of all molecules surrounding the point, say, within a small sphere with radius large compared with the mean distance between molecules is of the order n-1/3 cm. Molecular theory, however, must be used to calculate fluid properties (e.g., viscosity) which are associated with molecular motions, but continuum equations can be employed with the results of molecular calculations.

In rarefied gases, such as the atmosphere at 50 m above sea level, the ratio of the mean free path of the gas to a characteristic length for body or conduit is used to distinguish the type of flow. The flow regime is called gas dynamics for very small values of the ratio; the next regime is called slip flow; and for large values of the ratio it is free molecule flow. In this text only the gas-dynamics regime is studied.

The quantities density, specific valome, velocity, and acceleration are assumed to vary continuosly throughout a fluid (or be constant)

Properties of Fluids MASS DENSITY :For water at standard pressure (760 mm Hg) and 4oC (39.2oF), SPECIFIC WEIGHT : RELATIVE DENSITY : SPECIFIC VOLUME :

Viscosity

Pressure The normal force pushing against a plane area divided by the area is the average pressure. The pressure at a point is the ratio of normal force to area as the area approaches a small value enclosing the point. If a fluid exerts a pressure against the walls of a container, the container will exerts a reaction on the fluid which will be compressive. Liquids can sustain very high compressive, since this reason that the absolute pressure used in this book are never negative, since this would imply that fluid is sustaining a tensile stress. Pressure p has the units force per area, which may be newtons per aquare inch (psi). Pressure may also be expressed in terms of an equivalent height h of a fluid column, (Boyles and Charless laws)Where p is absolute pressure in pascals, specific volume vs per unit mass m3/kg, temperature T is the absolute temperature in degrees Kelvin (273 + degrees Celsius) and R is the gas constant in J/kg K. Since = 1 vs the above equation may be written

Bulk Modulus of ElasticityThe compressibility of a liquid is expressed by dp, it will cause a volume decrease dV; the ratio is the bulk modulus of elasticity K. For any volume V of liquid,Since is dimensionless, K is expressed in units of p. For water at 20oC, K = 2.2 GPa, or K=311,000 lb/in2 for water at 60oF.To gain some idea about the compressibility of water, consider the application of 0.1 MPa (about one atmosphere) to a cubic meter of water or about 45.5 cm3

Vapor Pressure VAPOR PRESSURELiquids evaporate because of molecules escaping from the liquid surface. The vapor molecules exert a partial pressure in the space, known as vapor pressure. If the space above the liquid is confined, after a sufficient time number of vapor molecules striking the liquid surface and condensing is just equal to the number escaping in any internal of time, and equilibrium exists. Since this phenomenon depends upon molecular activity, which is a function of temperature, the vapor pressure above a liquid equals the vapor pressure of the liquid, boiling occurs. Boiling of water, for example, may occur at room temperature if the pressure is reduced sufficiently. At 20oC water has a vapor pressure of 2.447 kPa and mercury has a vapor pressure of 0.173 Pa.

Surface Tension and Capillarity SURFACE TENSIONThe surface tension of water varies from about 0.074 N/m at 20oC to 0.059 N/m at 100oC CAPILLARITY

CHAPTER 02 DIMENTIONAL ANALYSIS

Newton

a

FUNDAMENTALS OF FLUID FLOW An ideal fluid is an imaginary fluid whose viscosity is zero. Flow may be steady or unsteady.In steady flow the flow characteristics at a fixed position in space do not change with time; pressure and velocity change only with the change of position of a fluid particle. Where the velocity subscripts denote the respective projections on a set of Cartesian axes.In the general case of unsteady flow, pressure and velocity vary with both position and time, i. e.,

Fluid FlowFluid flow may be :Steady vs. UnsteadyUniform vs. Non-uniformLaminer vs. TurbulentOne-dimensional, two-dimensional, three-dimensional

One, two and three-dimentional flowTrue one-dimentional flow of an incompressible fluid occurs when the direction and magnitude of yhe velocity at all points are identical. Two-dimentional occurs when the fluid particles move in the planes or parallel planes and the treamline patterns are identical in each plane.

Steady FlowSteady flow occurs if, at any point, the velocity of successive fluid paeticles is the same at successive oeriods of time. Thus, the velocity is constant with respect to time or

Uniform FlowUniform flow occurs when the magnitude and direction do not change from point to point in the fluid, or

Steady and Unsteady Flow In steady flow the fluid particles travel along pathlines which do not change with time. In unsteady flow different particles passing through a given point in space will be moving along different pathlines. Accordingly, to investigate the flow pattern for every given moment of time the concept of steamline is introduced.Fig. 23. SteamlineFig. 24. Stream tube

RATE OF DISCHAGE, EQUATION OF CONTINUITY The rate of discharge (commonly shortened to discharge or flow) is defined as the quantity of fluid flowing per unit time across any section of a stream. It may be expressed in units of volume, weight or mass : volume rate of discharge Q and weight rate of discharge G.m3/sec, Where dA = area of the cross-section;kg/sec const (along a stream tube)..const (along a stream tube).

BERNOULLIS EQUATION FOR A STREAM TUBE OF AN IDEAL LIQUID The sumis called the total head.Thus, the sum of the elevation, pressure and velocity heads of an ideal liquid is constant along a stream tube.

Elevation head, or potential head, or geodetic head;Pressure head, or static head;Velocity head.

Energy Line (EL) and Hydraulic Grade Line (HGL)

POWERP = rogQH H dalam J/N, P dlm J/s (watt)

Latihan Fluida 1800 liter per menit mengalir melalui pipa berdiameter 0,3 meter, pipa menyempit menjadi berdiameter 0,15 meter, hitung kecepatan rata-rata dalam pipa yang berukuran berbeda tersebut.V30 = 0,42 m/detV15 = 1,68 m/detAir mengalir dari A ke B dengan laju 0,4 m3/det dan head tekanan pada A sebesar 7 m. Dianggap tidak ada kehilangan energi selama mengalir dari A ke B, hitung head tekanan pada B. B lebih tinggi 5 m dari A.Sistem pemompaan air ditunjukkan pada Gambar, pompa BC harus mampu memompa minyak 0,16 m3/det, rl dn = 0,762 ke tampungan D. Dengan mengasumsikan kehilangan energi dari A ke B 2,5 J/N dan dari C ke D 6,5 J/N, berapa tenaga pompa yang harus digunakan.

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