Pressure
- Pressure is defined as the force acting normally per unit area.
- Pressure on an area, A is the area of the surface on contact and F is the normal force applied.
- Pressure is a scalar quantity.
\[P\,=\,\left( F/A \right)\]
- If the force is due to the weight (W) of the object, the equation is then:
\[P\,=\,W\,/\,A\]
- Hydrostatic pressure is the pressure that is executed by a fluid at equilibrium at a given point within the fluid, due to the force of gravity.
- Hydrostatic pressure equation is P = hdg where P = pressure \[(N/{{M}^{2}}\,or\,Pa)\], h =height (m), d = density\[(kg/{{m}^{3}})\], g = acceleration due to gravity \[(9.81\text{ }m/{{s}^{2}})\]
- The SI unit for pressure is the pascal. Pa, where \[1\,Pa=1\,N/{{m}^{2}}.\]
- The standard atmospheric pressure is measured in various units.
1 Atmosphere = 760 mmHg = 101.3 kpa
- The mercury barometer and other manometer devices are reliable pressure measurement devices. A "rising" barometer indicates increasing air pressure i.e. calm weather, a "falling" barometer indicates decreasing air pressure, i.e., inclement weather or harsh weather.
- Factors Affecting the Magnitude of Pressure
- Magnitude of the force: The larger the force, the higher the pressure.
- Contact area: The larger the contact area, the lower the pressure.
- The pressure at any level in the atmosphere may be interpreted as the total weight of the air above a unit area at any elevation.
Pascal's Principle
- Pascal's Principle is used to quantitatively relate the pressure at two points in an incompressible static fluid.
- It states that pressure is transmitted, undiminished, in a closed static fluid.
- The total pressure at any point within an incompressible, static fluid is equal to the sum of the applied pressure at any point in that fluid and the hydrostatic pressure changes due to a difference in height within that fluid.
Applications
- The underlying principle of the hydraulic pressure.
- Used for amplifying the force of the driver's foot in the braking system of most cars and trucks.
- Used in artesian wells, water towers, and dams.
- Scuba divers must understand this principle. At a depth of 10 metres under water, pressure is twice the atmospheric pressure at sea level, and increases by about 105 kPa for each increase of 10 m depth.
Surface Tension (T)
- Surface Tension (T): It is the property of a liquid by virtue of which it behaves like an elastically stretched membrane with a tendency to contract so as to occupy a minimum surface area.
- Mathematically \[T=\frac{F}{L}\]
F = Force per unit length
L = Length over which force acts
- I. Unit is : \[N{{m}^{-\,1}}\] and Dimensional formula is \[{{M}^{1}}{{L}^{0}}{{T}^{-\,2}}\]
Surface Energy
- The energy responsible for the phenomenon of surface tension may be thought of as approximately equivalent to the work or energy required to remove the surface layer of molecules in a unit area. The potential energy per unit area of the surface film is called the surface energy.
- Surface tension is numerically equal to surface energy. Its unit is N/m.
- An increase in temperature lowers the net force of attraction among molecules and hence decreases surface tension.
- The Surface of Water: Surface tension creates a thin elastic film on the surface of water.
- Surface Tension at the Molecular Level: A water molecule has one oxygen atom (0) and two hydrogen atoms (H). The negative end of the water molecule is attracted to the positive end of other water molecules. Under the surface of water these attractions balance out, but on the surface they are unbalanced. This is because the molecules on the surface have one surface exposed to the air and no other water molecules are there to balance out the charges. So, the surface molecules are pulled inward and surface tension is created.
- Breaking up Surface Tension: Surface tension can be broken by adding soap to water. Soap disrupts the surface tension causing the thin film to split and fly apart.
- Adhesive Forces: Forces of attraction between a liquid and a solid surface are called adhesive forces. Force of attraction between like molecules of surface are called the cohesive forces. The difference in strength between cohesive forces and adhesive forces determines the behaviour of a liquid in contact with a solid surface.
- Water does not wet waxed surfaces because the cohesive forces within the drops are stronger than the adhesive forces between the drops and the wax.
- Water wets glass and spreads out on it because the adhesive forces between the liquid and the glass are stronger than the cohesive forces within the water.
Capillary Action
- Capillary Action can be defined as the ability of liquid to flow through slim tube, cylinder or permeable substance due to adhesive and cohesive forces interacting between the liquid and surface.
- The liquid creeps up the inside of the tube (as a result of adhesive forces between the liquid and the inner walls of the tube) until the adhesive and cohesive forces of the liquid are balanced by the weight of the liquid.
- The smaller the diameter of the tube, the higher the liquid rises.
Buoyancy
- It is an upward force exerted by a fluid that opposes the weight of an immersed object.
Archimedes' Principle
- It states that when a body is immersed completely or partly in a fluid, it loses weight equal to the weight of the fluid displaced by it.
- Apparent weight of body = Actual Weight of Body – Upthrust
- Buoyant force depends on the density of the fluid and not on the density of body acting on centre of gravity of fluid.
Archimedes' Law of Floatation
- When a body is immersed in a fluid then:
- The weight W of body is more than the upthrust W’ (W > W’), the body will sink.
- The weight W of the body is equal to upthrust W’ (W = W), the body floats with whole of its volume inside the liquid.
- The weight (W < W’), the body will float with some of its part outside the liquid.
- When a block of ice floats in a liquid having density greater than that of water, the liquid level rises when all the ice melts into water.
- When an ice block floats in a liquid of density less than that of water, the liquid level falls when all the ice melts into water.
- When an ice block floats in water, the water level will remain the same when all the ice melts into water.
Equilibrium of Floating Body
- Stable equilibrium
- Unstable equilibrium
- Neutral equilibrium
Stable equilibrium: When a body is given a small angular displacement, i.e. it is tilted slightly by some external force and then it returns back to original position due to internal forces. Such equilibrium is called stable equilibrium.
Unstable equilibrium: If a body does not return to its original position from the slightly displaced angular position and moves farther away when given a small angular displacement, such equilibrium is called an unstable equilibrium.
Neutral equilibrium: The body remains at rest in any position to which it may be displaced, no net force tends to return the body to its original state or to drive it further away from the original position, is called neutral equilibrium.
Metacentre: When a small angular displacement is given to a body floating in a liquid, it starts oscillation about some point M. This point about which the body starts oscillating is called the metacentre.
Metacentric height: The distance between the centre of gravity of a floating body and the metacentre, i.e. distance GM is called meta-centric height. Relation between centre of gravity and metacentre in three different types of equilibrium:
- Stable equilibrium: In this equilibrium, the position of metacenter (M) remains higher than the centre of gravity of body.
- Unstable equilibrium: In this equilibrium, the position of metacenter (M) remains lower than the centre of gravity of body.
- Neutral equilibrium: In this equilibrium, the position of metacenter (M) coincides with the centre of gravity of body.
