Transcript Lecture01
What is Fluid?????
• A fluid may be liquid, vapour or gas. It has no permanent shape but takes up the shape of a containing vessel or channel or is shaped by external forces (eg the atmosphere). • A fluid consists of atoms/molecules in random motion (translation) and in continual collision with the surroundings. • Fluids are readily deformable, and flow.
• Solids have ‘frozen’ molecules that vibrate and do not translate. Solids resist change of shape.
What is Fluid?????
Attached plates Solid (Rectangular Block) B t t F T For a solid, application of a shear stress causes a deformation which, if modest, is not permanent and solid regains original position.
B F T
What is Fluid?????
Fluid at rest Sliding (shearing occur between fluid layer) F T For a fluid, continuous deformation takes place with an infinite number of layers sliding over each other. Deformation continues until the force is removed.
F T
What is Fluid?????
F T t o a) Solid 0 1. Primary Dimensions Primary dimension SI Unit Mass (M) Length (L) Time (T) Temperature (Q) BG Unit Conversion Factor Kilogram(kg) Meter(m) Second (s) Kelvin (K) Slug 1slug = 14.5939kg Foot (ft) 1 ft = 0.3048 m Second (s) 1 s = 1 s Rankine ® 1 K = 1.8 R Secondary Dimension velocity acceleration force energy (or work) power SI Unit . m/s m/s 2 N kg m/s 2 Joule J N m, kg m 2 /s 2 Watt W N m/s kg m 2 /s 3 ms ms -1 -2 kg ms -2 kg m 2 s -2 Nms -1 kg m 2 s -3 In primary dimension LT -1 LT -2 M LT -2 ML 2 T -2 ML 2 T -3 Secondary Dimension pressure ( or stress) density specific weight relative density SI Unit . Pascal P, N/m 2 , kg/m/s 2 kg/m 3 N/m 3 kg/m 2 /s 2 a ratio no units . Nm -2 kg m 1 s -2 kg m -3 kg m 2 s -2 In primary dimension ML -1 T -2 ML -3 ML -2 T -2 1 no dimension A fluid offers resistance of motion due to its viscosity or internal friction. Viscosity arises from movement of molecules from one layer to another moving at a different velocity. Slower layer tend to retard faster layers hence resistance Shear stress t F A Shear strain x y Rate of Shear strain t x ty t x 1 y u y For most fluids used in engineering it is found that the shear stress is directly proportional to rate of shear when straight and parallel flow is involved t u y t cons tan t u y where u y is velocity change in y direction So, at any point is the true velocity gradient du dy t du dy Newton's law of viscosity The constant of proportionality; is called the dynamic viscosity or just viscosity 1) 2) Determine the unit of dynamic viscosity; Kinematic viscosity; u is defined as the ration of dynamic viscosity to fluid density; Determine the unit of Kinematic viscosity Circular plate slides over the larger flat surface on a thin film of liquid that has a thickness of 0.02 mm. The plate has an diameter of d=6.3cm and mass of 20 g. If the plate is given an initial velocity of 5m/s, calculate the force required to move the plate at a steady velocity.Assume dynamic viscosity of liquid =1.805 kg/m-s u=5 m/s =1.805kg/m-s y=0.02 mm Surface A board 1m by 1m that weight 25 N slides down an inclined ramp (slope = 20 O ) with a velocity of 2.0 cm/s. The board is separated from the ramp by a thin film of oil with a velocity of 0.05 N.s/m2. Neglect the edge effect, calculate the spacing between the board and the ramp A board 1m by 1m that weight 25 N slides down an inclined ramp (slope = 20 O ) with a velocity of 2.0 cm/s. The board is separated from the ramp by a thin film of oil with a velocity of 0.05 N.s/m2. Neglect the edge effect, calculate the spacing between the board and the ramp A piston moves inside a cylinder at a velocity of 5 m/s, as shown in figure. The 150 mm diameter piston is centrally located within the 150.2 mm inside diameter cylinder. The film of oil separating the piston from the cylinder has an an absolute viscosity of 0.40 N.s/m2. Assuming a linear velocity profile, find the a) Shear stress in the oil b) Force F required to maintain the given motion c) Force by which the required force would change if the velocity increased by a factor of 2 Fluids which do not obey the Newton's law of viscosity are called as non-Newtonian fluids . Generally non-Newtonian fluids are complex mixtures: slurries, pastes, gels, polymer solutions etc., Variation of Viscosity with Temperature For gases o T T o n o T T o 3 / 2 ( T T S o S ) Power law Sutherland law Variation of Viscosity with Temperature For Liquid ae bT ln 0 a b T 0 T c T 0 T 2 For water T o = 273.16K, m o = 0.001792 kg/(m.s) and a = -1.94, b = -4.80 , c = 6.74 From a microscopic point of a view a fluid is not continuous and homogenous substance but consists of atom or molecules in random motion and with relatively large space between them. Under such circumstances it has no meaning refer to the velocity at a point in a fluid because that point may be empty space at particular instant. When we refer to the velocity of a fluid, we usually imply a quantity of fluid consisting of an enormous number of atoms of molecules-fluid velocity is a macroscopic concept. macroscopic microscopic X Fluid Average Density = m i v i Total Mass = m 1 Total Volume = V 1 Density at point = v lim 0 m V d m/ d V Average Density d V The weight per unit volume of a fluid is called its specific volume and equal to g, the product of its density and the acceleration of gravity g air = ( 1.204 kg/m 3 ) ( 9.807m/s 2 ) = 11.8N/m 3 or = 0.0752lbf/ft 3 g water = ( 998kg/m 3 ) ( 9.807m/s 2 ) = 9790N/m 3 or = 62.4lbf/ft 3 Specific gravity (SG) which is the ratio of density to the standard density of some reference fluid at 20 o C and 1 atm SG air gas air gas 1 . 204 kg / m 3 SG water liquid water liquid 998 kg / m 3 P P d P V V d V Bulk modulus (K) = (change in pressure) / (volumetric strain) Bulk modulus (K) = (change in pressure) / (volumetric strain) Where the volumetric strain is the ratio of the change in volume to the initial volume d V / V d P / K or K VdP / dV From the mass conservation; dm Vd dV 0 or So that K VdP V d dV ( V ) d or K dP d Typical values of Bulk Modulus: K = 2.05x10 9 N/m 2 for water K = 1.62 x 10 9 N/m 2 for oil.Dimensions and Unit
Dimensions and Unit
Dimensions and Unit
Viscosity
Viscosity
Viscosity
Viscosity
Viscosity
EXAMPLE 0
EXAMPLE 1
EXAMPLE 1.1
EXAMPLE 1
EXAMPLE 1.2
EXAMPLE 1.2
Viscosity
Viscosity
Viscosity
CONTIMUUM
DENSITY
DENSITY
Specific Weight
Specific Gravity
Compressibility and the Bulk modulus
Compressibility and the Bulk modulus
Compressibility and the Bulk modulus
Compressibility and the Bulk modulus