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:
V = \sqrt{2h \rho _{m} g/ \rho \thinspace [ A_1^2 / A_2^2 - 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 900, the liquid is considered non wetting.
* If the angle of contact is acute, that is, less than 900, 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.