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> 1.1 INTRODUCTION, , sane Se which deals with the behaviour of the fluids (liquids or, dynatnic aspects of fluids, Th on. Thus this branch of science deals with the static, kinematics and, motion, where pressure force, e study of fluids al rest is called fluid statics. The study of fluids in,, , ; $ are not considered, is called fluid kinematics and if the pressure forces, are also considered for the fluids in motion, that branch of science is called fluid dynamics., , , , p 1.2 PROPERTIES OF FLUIDS, , 1.2.1 Density or Mass Density, Density or mass density of a fluid is defined as the ratio of the, mass of a fluid to its volume. Thus mass per unit volume of a fluid is called density. It is denoted by the, symbol p (tho). The unit of mass density in SI unit is kg per cubic metre, i.c., kg/m’, The density of, liquids may be considered as constant while that of gases changes with the variation of pressure and, temperature., , Mathematically, mass density is written as, , _ _Mass of fluid f ut, ~ Volume of fluid * \, The value of density of water is 1 gm/cm’ or 1000 kg/m’, ‘|, , 1.2.2 Specific Weight or Weight Density. Specific weight or weight density of a fluid is the, ratio between the weight of a fluid to its volume, Thus weight per unit volume of a fluid is called, , weight density and it is denoted by the symbol w., icall we Weight of fluid _ (Mass of fluid) x Acceleration due to gravity, Thus mathematically, Volume of fluid ie, , , , _ Mass of fluid X g, ~~ Volume of fluid, , =PX8 I", , , , were (tl)

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tb 7 ——, , The value of specific weight or weight density (w) for water is 9.81 * 1000 Newton/m? in SI units., , , , 1.2.3 Specific Volume. Specific volume of a fluid is defined as the volume of a fluid occupied, by o unit mass oF volufie per unit mass of a fluid is called specific volume Mathematically, it is, expressed as, , , , . Volume of fluid _ 1 |, Specific volume = “Mass of fluid of fluid = Mass of Maid” ?, Volume of fluid, , Thus specific volume is the reciprocal of mass density. It is expressed as m’/kg. It is commonly, applied to gases., , 1.2.4 Specific Gravity, Specific gravity is defined as the ratio of the weight density (or density), of a fluid to the weight density (or density) of a standard fluid. For liquids, the standard fluid is taken, water and for gases, the standard fluid is taken air. Specific gravity is also called relative density. It is, dimensionless quantity and is denoted by the symbol 5., , Weight density (density) of liquid, , Mathematically, S(for liquids) = —— - Weight density (density) of water, , Weight density (density) of gas, Weight density (density) of air, ‘Thus weight density of a liquid = $ x Weight density of water, = 5x 1000 x 9.81 N/m”, ‘The density of a liquid = Sx Density of water, = $x 1000 kg/m’. (1.14), If the specific gravity of a fluid is known, then the density of the fluid will be equal to specific, gravity of fluid multiplied by the density of water. For example, the specific gravity of mercury is 13.6,, hence density of mercury = 13.6 x 1000 = 13600 kg/m’., , S(for gases) =, , Problem 1.1. Calculate the specific weight, density and specific gravity of one litre of a liquid, which weighs 7 N., , Solution, Given :, , 1 5 1 . 3, Volume = 1 litre = ——m* (: 1 ite=— 5 or 1 litre = 1000 cm, , 1000, Weight = 7N, (/) Specific weight (w) = = Weight ___7N__ _ 4999 N/m’. Ans., Volume 1 3, —|m, 1000, (ii) Density (p) #0 kg/m’ = 713.5 kg/m’, Ans., g 981, , a Density of liquid _ 1135 {1+ Density of water = 1000 kg/m’), , ~ Density of water 1000, = 0.7135, Ans., , (ii) Specific gravity

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i Oe, , Problem 1.2 Calc, ‘4 Calculate the density, specific weight and weight of one litre of petrol of specific, gravity = 0.7, , , , Solution. Given ; 1 1000,, Tne, , Volume = | litre = 1 x 1000 cm’ = m? = 0.001 m’, , Sp. gravity $=07 ", , (i) Density (p), , Using equation (1.1A),, , Density (p) = Sx 1000 kg/m? = 0.7 x 1000 = 700 kg/m’. Ans., (ii) Specific weight (w), , Using equation (1.1), w= px g = 700 x 9.81 Nim’ = 6867 Nim’, Ans., (iii) Weight (W), , , , We know that specific weight = Weight, Volume, of w= or 6867 =, 001 0.001, , W = 6867 x 0.001 = 6.867 N. Ans., , p> 1.3 VISCOSITY, , Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer, of fluid over another adjacent layer of the fluid. When two layers of a fluid, a distance “dy” apart, move, one over the other at different velocities, say u and u + du as shown in Fig. 1.1, the viscosity together, with relative velocity causes a shear stress acting between the fluid layers., , , , The top layer causes a shear stress on the, adjacent lower layer while the lower layer causes + |ueg /, a shear stress on the adjacent top layer. This shear dy Lu 7, stress is proportional to the rate of change of ve- 1 fi., , <, , locity with respect to y. It is denoted by symbol, , |, (Ta. | | “—VELOCITY PROFILE, du TITITTITTTTITT TOOT TTT, Mathematically, Te ay =e, de Fig. 1.1 Velocity variation near a solid boundary., T= a s€$.2), , where (called mu) isthe constant of proportionality and is known as the co-efficient of dynamic viscosity, if dm : inawonik ; . ., or only viscosity. a represents the rate of shear strain or.nate of shear deformation . Velocity gradient., , du sob}, dy, Thus viscosity is also defined as the shear stress required to produce unit rate of shear, s s, , 1.3.1 Units of Viscosity. The units of viscosity is obtained by putti :, YY puttin, <i, Quantities in equation (1.3) Putting the dimensio, , a ~, , t, From equation (1.2), we have }t = (*), , train, |, ns of the, , Generated Via PDF Scanner

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id EAaRSDIOAON cs, . Forve/ Area, , 12 Shear stress, we Change of velocity (aa) |, Change of distance Time / Length, , . Forve/(Length)” Forve x Tine, | (Length)?, Time, In MKS system, force is represented by kgf and length by metre (im), in CGS system, force is, em and in SI system force is represented by Newton (N) and length, , represented by dyne and length by, , by metre (m)., MKS unit of viscosity = = gis, m, _. dyne-sec, , CGS unit of viscosity ;, em, avn as Pascal which is represented by Pa, Hence N/m’ © Pa, , In the above expression Nim’ is also kno, , , , = Pascal, i SI unit of viscosity = Ns/in’ = Pa s., r er Newton-sec __ Ns, SI unit of viscosity = : <=, m nm, , The unit of viscosity in CGS is also called Poise which is equal to aes =,, en", f the unit of viscosity from MKS unit to CGS unitis given below :, {cc Ukgf = 9.81 Newton), , , , The numerical conversion 0, one kgf-sec _ 9.81N-sec |, , m? m, But one Newton = one kg (mass) X one (2) (acceleration), see, * (2000 gm) x (100.em) = 1000 x 100 a, io sec”, , sec, | = 1000 x 100 dyne ‘ dyne = gm X =, se, one wise = 9.81 x 100000 dyne-see _ 9 91x 100000 dyne-see, on? 100. 10x em, , m, a dynesee }, = 98,1 SHES = 98,1 poise vy QUES - Poise}, em 4 em J, it must be divided By B8-TW get, , / Thus for solving numerical problems, if viscosity is given in poise,, its equivalent numerical value in MKS., , , , , , , , 4, , , , one kgf-s 81 Ns ', But one kgf see. SBINS 98.1 poise pia, m m \ - \, one Ns c 98.1 51g 2 AO BEL One oii LNs ») \Y, — poise = se sea — ay., m 981 ms Bey tC" p 10 nv, , —~" :, , il

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Pe, , Alternate Method, One poise = 2, , But dyne, , uw, , 2. One poise eo, , : x 100 ot or | Me = 10 poise., D0) sm 10 sm sm, , ", s|, ', , Note, (i) In SL units second is represented by ‘s’ and not by ‘sec’., (ii) If viscosity is given in poise, it must be divided by 10 to get its, Sometimes a unit of viscosity as centipoise is used where, , equivalent numerical value in SI units., , : l | ar ., | centipoise © wise or 1cP2—~P cP = Centipoise, P = Poise}, st tog Pei | Pe, , The viscosity of water at 20°C is 0.01 poise or 1.0 centipoise,, , © ratio between the dynamic viscosity and density, , 1.3.2 Kinematic Viscosity. It is defined as th, of fluid. It is denoted by the Greek symbol (Vv) called ‘nu’, Thus, mathematically,, , , , = Viscosity J (1.4), ' Density Pp ' Py C, The units of kinematic viscosity is obtained as AY,, — Units oft _ Force x Time _ Force X Time of, : Mass SS, , , , , , © Unitsof P engthy? x — SS —, (Length) (Length)* Length, Length, , , , , , # Mass x “yx Time ‘Force ® Mass x Acc., (Time), , Length, Mass = Mass x Time?, , Length ime, , (Length)”, “Time 1 |, In MKS and SI, the unit of kinematic viscosity is metre*/sec or m/sec while in CGS units it is, , ‘oke,, , Ms, , written as cm?/s, In CGS units, kinematic viscosity is also knownas-s oe, = own, , sit Ly -4),2 \o, mest) som’/s = (x) ms 10 m Is yas v betel, a, , |, Centi ‘ = — stoke, =, ‘entistoke means 700 e, je, , 1.3.3 Newton's Law of Viscosity. It states that the shear stress (t) on a fluid element layer is, directly proportional to the rate of shear strain, The constant of proportionality is called the coefficient of viscosity, Mathematically, it is expressed as given by equation (1.2) or as, , du , ", , dy?