# Summary

- The basic property of a fluids is that it can flow. The fluid does not have any resistance to change of its shape. Thus, the shape of a fluid is governed by the shape of its container
- A liquid is incompressible and has a free surface of its own. A gas is compressible and it expands to occupy all the space available to it.
- If F is the normal force exerted by a fluid on an area, A then the average pressure P
_{av}is defined as the ratio of the force to area

P_{av}= F/A - The unit of pressure is the pascal (Pa). It is the same as Nm-
^{2}. Other common units of pressure are

1 atm = 1.01x10^{5 }Pa

1 bar = 10^{5}

1 torr = 133 Pa = 0.133 kPa

1 mm of Hg = 1 torr = 133 Pa - Pascal's law states that: Pressure in a fluid at rest is same at all points which are at the same height. A change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and the walls of the containing vessel.
- The pressure in a fluid varies with depth h according to the expression P =P
_{a}+ ρgh Where ρ is the density of the fluid, assumed uniform. - The volume of an incompressible fluid passing any point every second in a pipe of non uniform crosssection is the same in the steady flow. vA = constant ( v is the velocity and A is the area of crossection ) The equation is due to mass conservation in incompressible fluid flow.
- Bernouli's principle states that as we move along a streamline, the sum of the pressure (P), the kinetic energy per unit volume (ρv
^{2}/2) and the potential energy per unit volume ( ρgy) remains a constant. Ρ + ρv^{2}/2 + ρgy = constant - The equation is basically the conservation of energy applied to non viscuss fluid motion in steady state. There is no fluid which have zero viscosity, so the above statement is true only approximately. The viscosity is like friction and converts the kinetic energy to heat energy.
- Though shear strain in a fluid does not require shear stress, when a shear stress is applied to a fluid, the motion is generated which causes a shear strain growing with time. The ratio of the shear stress to the time rate of shearing strain is known as cofficient of viscosity, η. Where symbols have their usual meaning and are defined in the text.
- Stoke's law states that the viscous drag force
**F**on a sphere of radius a moving with velocity**v**through a fluid of viscosity is**F**= -6∏ηav - The oneset of turbulence in a fluid is determined by a dimensionless parameter is called the Reynolds number given by

- Surface tension is a force per unit length (or surface energy per unit area) acting in the plane of interface between the liquid and the bounding surface. It is the extra energy that the molecules at the interface have as compared to the interior.