BASIC FLUID MECHANICS DR.SATISH KUMAR DEPARTMENT OF MECHANICAL ENGINEERING 2014 NIT JAMSHEDPUR - Copyright 2013 Copyright Wednesday, July 31, 2019 1 Fluid Mechanics • Fluid mechanics is that branch of science which deals with the behavior of fluids (liquid &gasses) at rest and motion. • Basically a study of the: – Physically behavior of fluids and fluid systems , and of the laws governing this behavior. – Action of forces on fluid and of the resulting flow 2014 pattern. - Copyright 2013 Copyright FLUID Fluid is defined as one which under continuously applied tangential stress, starts deforming continuously as long as shear stress is applied. In other words, it can flow continuously as a result of shearing action. This includes any liquid or gas. 2014 - Copyright 2013 Copyright 3 What is a Fluid? Fluid: A substance in the liquid or gas phase. A solid can resist an applied shear stress by deforming. A fluid deforms continuously under the influence of a shear stress, no matter how small. In solids, stress is proportional to strain, but in fluids, stress is proportional to strain rate. Deformation of a rubber block placed When a constant shear force is applied, a solid eventually stops between two parallel plates under the deforming at some fixed strain influence of a shear force. The shear angle, whereas a fluid never stops stress shown is that on the rubber— 2014 deforming and approaches a an equal but opposite shear stress - constant rate of strain. acts on the upper plate. Copyright 2013 Copyright 4 Stress: Force per unit area. Normal stress: The normal component of a force acting on a surface per unit area. Shear stress: The tangential component of a force acting on a surface per unit area. Pressure: The normal stress in a fluid at rest. Zero shear stress: A fluid at rest is at a state of zero shear stress. When the walls are removed or a liquid container is tilted, a shear develops as the liquid moves to re- 2014 establish a horizontal free surface. The normal stress and shear stress at - the surface of a fluid element. For fluids at rest, the shear stress is zero and pressure is the only normal stress. 2013 Copyright 5 In a liquid, groups of molecules can move relative to each other, but the volume remains relatively constant because of the strong cohesive forces between the molecules. As a result, a liquid takes the shape of the container it is in, and it forms a free surface in a larger container in a gravitational field. A gas expands until it encounters the walls of the container and fills the entire available space. This is because the gas molecules are widely spaced, and the cohesive forces between them are very small. Unlike liquids, a gas in an open container cannot form a free surface. Unlike a liquid, a gas does not form a 2014 free surface, and it - expands to fill the entire available space. 2013 Copyright 6 Intermolecular bonds are strongest in solids and weakest in gases. Solid: The molecules in a solid are arranged in a pattern that is repeated throughout. Liquid: In liquids molecules can rotate and translate freely. Gas: In the gas phase, the molecules are far apart from each other, and molecular ordering is nonexistent. 2014 The arrangement of atoms in different phases: (a) molecules are at relatively fixed - positions in a solid, (b) groups of molecules move about each other in the liquid phase, and (c) individual molecules move about at random in the gas phase. 2013 Copyright 7 Gas and vapor are often used as synonymous words. Gas: The vapor phase of a substance is customarily called a gas when it is above the critical temperature. Vapor: Usually implies that the current phase is not far from a state of condensation. Macroscopic or classical approach: Does not require a knowledge of the behavior of individual molecules and provides a direct and easy way to analyze engineering problems. Microscopic or statistical approach: Based on the average behavior of large groups of individual molecules. On a microscopic scale, pressure is determined by the interaction of 2014 individual gas molecules. However, - we can measure the pressure on a macroscopic scale with a pressure 2013 Copyright gage. 8 Fluid Flow • The tendency of continuous deformation of fluid is called fluidity. • The act of continuous deformation is called flow . • Flow means that the constituent fluid particles continuously change their positions relative to one another. 2014 - Copyright 2013 Copyright Application Areas of Fluid Mechanics 2014 Fluid dynamics is used extensively in - the design of artificial hearts. Shown here is the Penn State Electric Total 2013 Copyright Artificial Heart. 10 11 Copyright 2013-2014 12 Copyright 2013-2014 Fluids Copyright 2013-2014 Vehicles Aircraft Surface ships High-speed rail Submarines 2014 - Copyright 2013 Copyright Air pollution Environment River hydraulics River Copyright 2013-2014 Blood pump Physiology and and Medicine Physiology Ventricular assistdevice Ventricular Copyright 2013-2014 Sports & Recreation Water sports Cycling Offshore racing Auto racing Surfing 2014 - Copyright 2013 Copyright History Faces of Fluid Mechanics Archimedes Newton Leibniz Bernoulli Euler (C. 287-212 BC) (1642-1727) (1646-1716) (1667-1748) (1707-1783) 2014 - Navier Stokes Reynolds Prandtl Taylor (1785-1836) (1819-1903) (1842-1912) (1875-1953) (1886-1975) Copyright 2013 Copyright Wednesday, July 31, 2019 Wednesday, PROPERTIES OF FLUID OF PROPERTIES 19 Copyright 2013-2014 SPECIFIC GRAVITY The specific gravity (or relative density) can be defined in two ways: Definition 1: A ratio of the density of a liquid to the density of water at standard temperature and pressure (STP) (20°C, 1 atm), or Definition 2: A ratio of the specific weight of a liquid to the specific weight of water at standard temperature and pressure (STP) (20°C, 1 atm), ρ γ SG = liquid = liquid ρwater @STP γ water @STP 2014 - Unit: dimensionless. Copyright 2013 Copyright Example A reservoir of oil has a mass of 825 kg. The reservoir has a volume of 0.917 m3. Compute the density, specific weight, and specific gravity of the oil. Solution: mass m 825 ρ = = = = 900kg / m3 oil volume ∀ 0.917 weight mg γ = = = ρg = 900x9.81 = 8829N / m3 oil volume ∀ 2014 ρoil 900 - SGoil = = = 0.9 ρw@ STP 1000 Copyright 2013 Copyright Viscosity • Viscosity, µ, is a measure of resistance to fluid flow as a result of intermolecular cohesion. In other words, viscosity can be seen as internal friction to fluid motion which can then lead to energy loss. • Different fluids deform at different rates under the same shear stress. The ease with which a fluid pours is an indication of its viscosity. Fluid with a high viscosity such as syrup deforms more slowly than fluid with a low viscosity such as water. The viscosity is also known as dynamic viscosity. Units: N.s/m2 or kg/m/s 2014 . Typical values: - Water = 1.14x10-3 kg/m/s; Air = 1.78x10-5 kg/m/s Copyright 2013 Copyright Newtonian and Non-Newtonian Fluid obey refer Fluid Newton’s law Newtonian fluids of viscosity Newton’s’ law of viscosity is given by; Example: Air du Water τ = µ Oil Gasoline dy Alcohol Kerosene τ = shear stress Benzene µ = viscosity of fluid Glycerine du/dy = shear rate, rate of strain or velocity gradient 2014 • The viscosity µ is a function only of the condition of the fluid, particularly its - temperature. • The magnitude of the velocity gradient (du/dy) has no effect on the magnitude of µ. Copyright 2013 Copyright Wednesday, July 31, 2019 Wednesday, VISCOSITY VISCOSITY 24 Copyright 2013-2014 Wednesday, July 31, 2019 Wednesday, VISCOSITY 25 Copyright 2013-2014 Newtonian and Non-Newtonian Fluid Do not obey Fluid Newton’s law Non- Newtonian of viscosity fluids •The viscosity of the non-Newtonian fluid is dependent on the velocity gradient as well as the condition of the fluid. Newtonian Fluids . a linear relationship between shear stress and the velocity gradient (rate of shear), . the slope is constant . the viscosity is constant 2014 - non-Newtonian fluids . slope of the curves for non-Newtonian fluids varies Copyright 2013 Copyright TYPES OF FLUIDS Newtonian fluids: these fluids follow Newton’s viscosity. For such fluids viscosity does not change with rate of deformation. For e.g. Water, kerosene, air etc Non-Newtonian fluids: Fluids which do not follow the linear relationship between shear stress and rate of deformation are termed as Non-Newtonian fluids. For e.g. Solutions or suspensions, mud flows, polymer solutions, blood etc. these fluids are generally complex mixtures and are studied under rheology a science of deformation of flow. 2014 Plastic fluids: In the case of a plastic substance which is non-Newtonian an initial yield - stress is to be exceeded to cause a continuous deformation. Copyright 2013 Copyright Wednesday, July 31, 2019 27 TYPES OF FLUIDS • A generalized Power-law model can describe both Newtonian and Non-Newtonian fluid as following: n du τ =AB + dy (i) When n = 1, B = 0, it is Newtonian fluid. (ii) When n > 1, the fluid is dilatants, i.e., quicksand, butter, printing ink. (iii) When n < 1, the fluid is pseudo plastic, i.e., gelatin, blood, milk, paper pulp, etc. 2014 (iv) When n = 1, B ≠ 0, the fluid is Bingham plastic, i.e., sewage - sludge, drilling muds,etc. Copyright 2013 Copyright Wednesday, July 31, 2019 Wednesday, TYPES OF FLUIDS TYPES OF 29 Copyright 2013-2014 Variation of viscosity with temperature • In the case of gases, increased temperature makes the molecular movement more vigorous and increases molecular mixing so that the viscosity increases. • In the case of a liquid, as its temperature increases molecules separate from each other, decreasing the attraction between them, and so the viscosity decreases.