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- Fluid Mechanics - FM
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**West Bengal University of technology - WBUT**- Mechanical Engineering
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1 Fluid Statics &RQWHQWV )OXLG 3URSHUWLHV 3DVFDO¶V /DZ )OXLG 6WDWLF (TXDWLRQ 3UHVVXUH PHDVXUHPHQW 5HVXOWDQW IRUFH RQ SODQH VXUIDFHV 5HVXOWDQW IRUFH RQ FXUYHG VXUIDFHV %XR\DQF\ 6WDELOLW\ FULWHULD IRU IORDWLQJ REMHFWV 7XWRULDO SUREOHPV 1.1 Fluid Properties Fluid A fluid is a substance, which deforms when subjected to a force. A fluid can offer no permanent resistance to any force causing change of shape. Fluid flow under their own weight and take the shape of any solid body with which they are in contact. Fluids may be divided into liquids and gases. Liquids occupy definite volumes. Gases will expand to occupy any containing vessel. S.I Units in Fluids The dimensional unit convention adopted in this course is the System International or S.I system. In this convention, there are 9 basic dimensions. The three applicable to this unit are: mass, length and time. The corresponding units are kilogrammes (mass), metres (length), and seconds (time). All other fluid units may be derived from these. Density The density of a fluid is its mass per unit volume and the SI unit is kg/m3. Fluid density is temperature dependent and to a lesser extent it is pressure dependent. For example the density of water at sea-level and 4oC is 1000 kg/m3, whilst at 50oC it is 988 kg/m3. 1

The relative density (or specific gravity) is the ratio of a fluid density to the density of a standard reference fluid maintained at the same temperature and pressure: ρ gas For gases: RDgas = For liquids: RDliquid = ρ air = ρ liquid ρ water ρ gas 1205 . kg / m 3 = ρ liquid 1000 kg / m 3 Viscosity Viscosity is a measure of a fluid’s resistance to flow. The viscosity of a liquid is related to the ease with which the molecules can move with respect to one another. Thus the viscosity of a liquid depends on the: • Strength of attractive forces between molecules, which depend on their composition, size, and shape. • The kinetic energy of the molecules, which depend on the temperature. Viscosity is not a strong function of pressure; hence the effects of pressure on viscosity can be neglected. However, viscosity depends greatly on temperature. For liquids, the viscosity decreases with temperature, whereas for gases, the viscosity increases with temperature. For example, crude oil is often heated to a higher temperature to reduce the viscosity for transport. Consider the situation below, where the top plate is moved by a force F moving at a constant rate of V (m/s). G\ 0RYLQJ SODWH 9 PV ) 9HORFLW\ GY )L[HG SODWH The shear stress τ is given by: τ = F/A The rate of deformation dv (or the magnitude of the velocity component) will increase with distance above the fixed plate. Hence: τ = constant x (dv / dy) 2

where the constant of proportionality is known as the Dynamic viscosity (µ) of the particular fluid separating the two plates. τ = µ x ( V / y) Where V is the velocity of the moving plate, and y is the distance separating the two plates. The units of dynamic viscosity are kg/ms or Pa s. A non-SI unit in common usage is the poise where 1 poise = 10-1 kg/ms Kinematic viscosity (ν) is defined as the ratio of dynamic viscosity to density. i.e. ν = µ/ρ (1.1) The units of kinematic viscosity are m2/s. Another non-SI unit commonly encountered is the “stoke” where 1 stoke = 10-4 m2/s. 3

Dynamic Viscosity Kinematic Viscosity Centipoise* (cp) Centistokes (cSt) Water 1 1 Vegetable oil 34.6 43.2 SAE 10 oil 88 110 SAE 30 oil 352 440 Glycerine 880 1100 SAE 50 oil 1561 1735 SAE 70 oil 17,640 19,600 Typical liquid Table 1.1 Viscosity of selected fluids at standard temperature and pressure Note: 1 cp = 10-3kg/ms and 1cSt = 10-6 m2/s Figure 1.1 Variation of the Viscosity of some common fluids with temperature Worked Example 1.1 The temperature dependence of liquid viscosity is the phenomenon by which liquid viscosity tends to decrease as its temperature increases. Viscosity of water can be predicted with accuracy to within 2.5% from 0 °C to 370 °C by the following expression: 4

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