**A Fluid is a substance which is capable of flowing under the action of shear force. The space between fluid molecules is relatively large. E.g. liquid, gases, vapor etc.**

Their intermolecular forces are low and fluid continuously undergoes deformation.

**Ideal Fluid:** It has no viscosity, no surface tension & incompressible

**Real Fluid:** It possesses the properties like viscosity, surface tension & compressibility

##### For a static fluid shear force is zero. Solid objects regain their original shapes after the force is removed if the shear force is within the elastic limit.

**Cohesive force:** Attraction between two similar molecules is known as cohesive force.

**Adhesive force:** Attraction between two different molecules is known as adhesive force.

__Density or mass density (ρ):__ It is defined as the ratio of mass of the fluid to its volume.It’s unit is kg/m³.

__Density or mass density (ρ):__

##### Note: Density of water 1000kg/m³

__ Density variation with temperature and pressure. __

__Density variation with temperature and pressure.__

**Temperature ↓**** ⇒ ****Density(ρ) ↑**

**Pressure ****↑ ****⇒ ****Density(ρ) ↑ **

__Specific weight or weight density (γ):__ It is defined as the ratio of weight of the fluid to its volume.It’s unit is N/m³.

__Specific weight or weight density (γ):__

__Specific gravity or Relative density (s):__ It is defined as the ratio of specific weight of the fluid to specific weight of a standard fluid.Standard fluid is water in case of fluid and air in case of gas.

__Specific gravity or Relative density (s):__

#### It’s is dimensionless.

__Specific volume :__ It is defined as the ratio of volume per unit mass.It’s unit is m³/kg.

__Specific volume :__

##### Fluid pressure at a point in stationary fluid is the force acting on any area or surface is perpemdicular to that surface.

**P = dF/dA**

##### If force is uniformly distributed over surface area then

##### P = F/A

##### It’s unit is Pascal(Pa).

**Pascal’s Law:**

#### According to this law pressure at a point in static fluid( fluid at rest) is equal in all directions.

### If fluid is static then **by pascal’s law**

**Px = Py= Pz**

**Hydrostatic’s Law**

##### According to this law, the rate of increase in pressure in a vertical direction is equal to the weight density of the fluid at that point.

Now integrating the above expression from z = 0 to z = h then pressure at depth h is given by

**P = ρgh**

**Relationship between pressures**

**Absolute pressure = Atmospheric Pressure + Gauge Pressure****Absolute pressure = Atmoshpheric Pressure – Vaccum pressure**

**Now let’s discuss few cases to measure the gauge pressure.**

**1.** We want to find the pressure at point B in the following figure:

As we have discussed above that pressure at C will be given by Hydrostatic law

Pc = ρgh

and by pascal’s law Pressure at any point in same level will be same i.e.

**Pb = Pc = ρgh**

**2.** We want to find the pressure at point B in the following figure:

By pascals law pressure will be same along A-A’ line.

Now applying hydrostatic law we can write

**3.** We want to find the pressure between points A& B in the following figure:

By pascals law pressure will be same along C-C’ line.

Now applying hydrostatic law we can write

#### Now we will see a case from which questions usually comes in exams

**4.** We want to find the pressure at point B in the following figure:

By pascals law pressure will be same along C-C’ line.

Now applying hydrostatic law we can write