Mechanical Properties of Fluids Physical quantities –fluids A fluid is any matter that has tendency to flow. All liquids and gases are together referred to as fluids. External force acting per unit area on a solid is called stress. Pressure is defined as force exerted per unit area. Density of a fluid is the ration of its mass to its volume. Variation in pressure atmospheric pressure; gauge pressure The pressure on an object submerged in a liquid is independent of the area of cross section. Atmospheric pressure at any point is equal to the weight of a vertical column of air of unit cross sectional area extending from that point to the top of the earth’s atmosphere. Gauge pressure is the difference between absolute pressure and atmospheric pressure at any given point. Gauge pressure is the same at all points at the same horizontal level or depth. Atmospheric pressure can be measured using a barometer or an open tube manometer. Archimedes’ Principle: when a body is partially or completely immersed in a fluid at rest, the fluid exerts an upward force of buoyancy, which is equal to the weight of the displaced fluid. Pascal’s law and hydraulic machines Pascal’s law: when external pressure is applied at a point in a fluid contained in a vessel, it is transmitted undiminished and equally in all directions. A number of devices such as a hydraulic lift, hydraulic press and hydraulic brakes work according to pascal’s law. Streamline flow The path taken by a particle in a flowing fluid is called its line of flow. The direction of motion of the particle is given by the tangent at that particular point of the particle. The flow of the fluid is said to be steady or laminar if all the particles passing a given point maintain steady velocity at that point. The path taken by a fluid particle in a steady flow is called a streamline. Fluids flowing through different tubes of flow do not intermix. The equations of continuity is valid as the product of area of cross section and its speed remains at the same at all points of a tube of flow. The equation of continuity represents the conservation of mass in the case of moving fluids. In a turbulent flow, the velocity of a particle at a point in a fluid varies with time. Critical velocity is the velocity of a liquid at which its flow changes from laminar to turbulent. Bernoulli’s principle All fluids possess three types of energy, namely, pressure energy, kinetic energy and potential energy. Bernoulli’s principle states that “for a streamline flow of an ideal liquid, the total energy per unit mass remains constant at every cross section throughout the flow”. Bernoulli’s principle holds good for all ideal liquids in a streamline flow. In the streamline flow of an ideal liquid, the sum of the pressure energy per unit volume, potential energy per unit volume and kinetic energy per unit volume is always a constant at all cross sections of the liquid. Torricelli’s law A fluid’s outflow from a tank is known as efflux. According to Torricelli’s law, the speed of a liquid coming out through a hole at a depth ‘h’ below the free surface is the same as that of a body dropped freely through height ‘h’ under gravity. The velocity of efflux is maximum when the depth of the orifice is at a maximum vertical distance from the free surface of the liquid. Venturimeter A venturimeter is a device used to measure the speed at which an incompressible fluid flows. Using the venturimeter principle, the speed of flow can be calculated using the expression: 2 2 V=√2hρmg/ρ [A 1/A 2 -1] Where: A1 = Area of cross section of larger tube of venturimeter A2 = Area of cross section of smaller tube of venturimeter h = Difference of the liquid level in the two arms of the manometer tube ρ = Density of liquid in venturimeter ρm =Density of liquid in venturimeter Blood flow and heart attack Blood pressure is the pressure due to the force exerted by circulating blood on the walls of blood vessels. Blood pressure is commonly measured in torr or mm of Hg. 1 mm of Hg= 1 torr= 0.133kPa Blood pressure is measured using a sphygmomanometer. Blood pressure is usually measured at a person’s upper arm. Dynamic lift Buoyant force is the force acting vertically upwards on a body immersed in a fluid. When a buoyant force acts on a body immersed in a fluid at rest, the body experiences a static lift. When a buoyant force acts on a body immersed in a fluid in motion, the body experiences a dynamic lift. An aerofoil is a solid piece shaped to provide an upward dynamic lift when it moves horizontally through air. Viscosity Viscosity is the resistance to fluid motion or the internal friction that regards the flow of the fluid. A viscous force exists when there is relative motion between layers of the fluid. The coefficient of viscosity (ɳ) is the ratio of the shear stress to strain rate. The viscosity of liquids decreases with an increase in temperature. Viscosity is normally independent of pressure. Stoke’s law Reynolds number Stoke’s law states that “At low velocities, the frictional force on a spherical body moving through a fluid at constant velocity is equal to 6π times the product of the velocity, the fluid viscosity, and the radius of the sphere”. Reynolds number is the ratio of total inertia forces to viscous force. Reynolds number for a liquid flowing through a tube is given by the expression Re= ρvd/ɳ ρ= Density of the liquid ѵ= Velocity of the liquid d= Diameter of the tube ɳ=Coefficient of viscosity of the liquid Surface tension and surface energy Force due to surface tension makes a drop or bubble assume a spherical shape. A cohesive force is the force of attraction between the molecules of the same distance. An adhesive force is the force of attraction between the molecules of different substances. The sphere within which molecular forces act on a given molecules is referred to as the sphere of influence. Surface tension can also be defined as the work done per unit increase in area of a liquid or surface energy per unit increase in area of the liquid. The surface tension of a liquid decreases with an increase in its temperature. Angle of contact The angle between tangent to the liquid surface at the point of contact and solid surface inside the liquid is defined as angle of contact. It is denoted by ⍬. The angle of contact, ⍬, depends on the nature of the liquid and solid in contact and the medium above the free surface of the liquid. The angle of contact is fixed for a given set of solids, liquids and surrounding media, usually, air. If the angle of contact is obtuse, that is, more than 90 0, the liquid is considered non wetting. If the angle of contact is acute, that is, less than 90 0, the liquid is considered wetting. If the angle of contact is zero, the liquid is considered absorbing. Drops and bubbles For a drop, the difference between the pressure inside the liquid drop and that of the outside air is equal to 2S/R. For a cavity, the difference between the air pressure inside the cavity and that outside liquid is equal to 2S/R. For a bubble, the difference between air pressure inside the bubble and that outside the bubble is equal to 4S/R. Capillary rise A capillary tube is a hollow tube with a very narrow bore. The rise or fall of a liquid in a capillary tube is called capillary action or capillarity. If the angle of contact of the liquid with the surface of the tube is an acute angle, there is a capillary rise. If the angle of contact of the liquid with the surface of the tube is an obtuse angle, there is a capillary fall. h=2s/ρrg Root hairs of plants absorb water from the soil by capillary action. .