Properties of a fluid
- the atoms and molecules of a fluid are arranged in a random manner.
- A fluid cannot withstand a tangential or a shearing force for long. It begins to flow when in contact with a shearing force.
- A fluid has no shape of its own. It assumes the shape of its container and so has no modulus of rigidity
- A fluid cannot exert a force perpendicular to its surface so a fluid has no bulk modulus of rigidity.
Thrust
thrust is the total force applied to any surface by a liquid in contact with it.
angle theta for a liquid at rest.
a liquid at rest always exerts a force perpendicular to the surface of the container at all points, when in equilibrium.
Pressure
Presuusre is the thrust acting normally per unit area about a point.
P=F/A
scalar quantity
si unit: N/m^2
CGS unit: dyne/cm^2
Dimensional formula: ML-1 T-1
Density
Density is the mass of a material per unit volume
p=M/V
scalar quanity
Si unit: kg/m^3
CGS unit: g/cm^3
Dimensional formula: ML-3T0
Specific Gravity/ Relative Density
Ratio of the density of the substance to the density of the water at 4 degrees celcius. Denisty of water=1000kg/m^3
Pascal’s Law
Pascal’s law suggests that the pressure exerted at any point in an enclosed liquid is transmitted equally in all directions.
Hydraulic LIft
Pressure exerted by a liquid column
effect of gravity on liquid pressure
conclusions of effect of gravity on liquid pressure
- the liquid pressure is the same at all points at the same horizontal level or at the same depth.
- Pressure at any point in the liquid depends on the depth, h.
- The absolute pressure, at a depth h, below the liquid surface exposed to the atmosphere is greater than the atmospheric pressure by a value pgh. Thsi is guage pressure
- Pressure doesn’t depend on the cross-sectional area or base-area of the vessel.
Mercury Barometer
Absolute pressure
total pressure or teh actual pressure P at a point
Guage Pressure
difference between the actual pressure at a point and the atmospheric pressure.
Buoyancy
Buoyancy is the upward force acting on a body emmersed in a fluid. It is also called upward thrust.
Archimedes’ Principle
It states that when a body is completely or partially immersed in a liquid, it experiences an upthrust which is equal to the weight of the fluid displaced by it and the upthrust acts through the centre of gravity of the displaced fluid.
Viscosity
Viscosity is the property of a liquid by virtue of which an internal force comes to play when a fluid is motion which opposes the motion between its different lasyers.
v= F/ A*dv/dx
STroke’s Law
the backward viscous forces acting on a small spherical body of radius r moving with uniform velocity v through a fluid of viscosity V is given by:
F=6piVrv
Terminal Velocity
Streamline Flow
When a liquid flows such that each particle of the liquid passing a given point moves along the same path and has the same velocity as its predecessor.
Turbulent Flow
After a certain critical velocity, the liquid flow becomes zig-zag and the path and the velocity of the liquid changes constantly.
properties of streamlines
steady flow; no two streamlines can cross each other
tangent gives direction of velocity
greater the no. of fluid streamlines passing through a point, larger the fluid velocity of the section
fluid velocity stays constant at any point.
laminar flow
when the velocity is less than the critical veloicty, each layer of the liquid slides over the other.
critical velocity
the critical velocity is that value of a fuluid’s velocity of low upto which the flow of the fluid streamlined and above which it becomes turbulent.
v== kn/pD
