# FLUID STATICS

**Fluid Mechanics is basically a study of**:

1) Physical behavior of fluids and fluid systems and laws governing their behavior.

2) Action of forces on fluids and the resulting flow pattern.

Fluid is further sub-divided in to liquid and gas. The liquids and gases exhibit different characteristics on account of their different molecular structure. Spacing and latitude of the motion of molecules is large in a gas and weak in liquids and very strong in a solid. It is due to these aspects that solid is very compact and rigid in form, liquid accommodates itself to the shape of the container, and gas fill up the whole of the vessel containing it.

## Fluid mechanics cover many areas like:

1. Design of wide range of hydraulic structures (dams, canals, weirs etc) and machinery (Pumps, Turbines etc).

2. Design of complex network of pumping and pipe lines for transporting liquids. Flow of water through pipes and its distribution to service lines.

3. Fluid control devices both pneumatic and hydraulic.

4. Design and analysis of gas turbines and rocket engines and air–craft.

5. Power generation from hydraulic, stream and Gas turbines.

6. Methods and devices for measurement of pressure and velocity of a fluid in motion.

## UNITS AND DIMENSIONS:

A dimension is a name which describes the measurable characteristics of an object such as mass, length and temperature etc. a unit is accepted standard for measuring the dimension. The dimensions used are expressed in four fundamental dimensions namely Mass, Length, Time and Temperature.

Mass (M) – Kg

Length (L) – m

Time (T) – S

Temperature (t) – ^{0}C or K (Kelvin)

**1. Density:** Mass per unit volume=kg/m3

**2. Newton:** Unit of force expressed in terms of mass and acceleration, according to Newton’s 2nd law motion. Newton is that force which when applied to a mass of 1 kg gives an acceleration 1m/Sec2. F=Mass x Acceleration = kg – m/sec2 = N.

**3. Pascal:** A Pascal is the pressure produced by a force of Newton uniformly applied over an area of 1 m2. Pressure = Force per unit area = N/ m2 = Pascal or Pa.

**4. Joule:** A joule is the work done when the point of application of force of 1 Newton is displaced Work = Force per unit area = N m = J or Joule.

**5. Watt: **A Watt represents a work equivalent of a Joule done per second. Power = Work done per unit time = J/ Sec = W or Watt.

## Density or Mass Density

The density or mass density of a fluid is defined as the ratio of the mass of the fluid to its volume. Thus the mass per unit volume of the fluid is called density. It is denoted by ℓ

The unit of mass density is Kg/m3

The value of density of water is 1000Kg/m3.

## Specific weight or Specific density

It is the ratio between the weights of the fluid to its volume. The weight per unit volume of the fluid is called weight density and it is denoted by w.

## Specific weight or Specific density

It is defined as the volume of the fluid occupied by a unit mass or volume per unit mass of fluid is called Specific volume.

Thus the Specific volume is the reciprocal of Mass density. It is expressed as m3/kg and is commonly applied to gases.

## Specific Gravity

It is defined as the ratio of the Weight density (or density) of a fluid to the Weight density (or density) of a standard fluid. For liquids the standard fluid taken is water and for gases the standard liquid taken is air. The Specific gravity is also called relative density. It is a dimension less quantity and it is denoted by ѕ.

Weight density of liquid=S × weight density of water = S×1000 ×9.81 N/ m 3

**Density of liquid= S × density of water = S × 1000 Kg/ m 3**

If the specific gravity of fluid is known, then the density of fluid will be equal to specific gravity of the fluid multiplied by the density of water

**Example:** The specific gravity of mercury is 13.6

Hence density of mercury = 13.6 ×1000 = 13600 Kg/ m 3

# VISCOSITY

It is defined as the property of a fluid which offers resistance to the movement of one layer of the fluid over another adjacent layer of the fluid. When the two layers of a fluid, at a distance ‘dy’ apart, move one over the other at different velocities, say u and u+du. The viscosity together with relative velocities causes a shear stress acting between the fluid layers.

The top layer causes a shear stress on the adjacent lower layer while the lower layer causes a shear stress on the adjacent top layer.

This shear stress is proportional to the rate of change of velocity with respect to y. it is denoted by symbol τ (tau).

Where μ is the constant of proportionality and is known as the co-efficient of **dynamic viscosity or ****only viscosity**.

**du/dy** represents the rate of shear strain or rate of shear deformation or velocity gradient.

From the above equation, we have

Thus, viscosity is also defined as the shear stress required producing unit rate of shear strain. The unit of viscosity in CGS is called poise and is equal to dyne-see/ cm2

## KINEMATIC VISCOSITY

It is defined as the ratio between dynamic viscosity and density of fluid. It is denoted by symbol 𝜗 (nu)

## NEWTONS LAW OF VISCOSITY

It states that the shear stress (τ) on a fluid element layer is directly proportional to the rate of shear strain. The constant of proportionality is called the co- efficient of viscosity. It is expressed as:

Fluids which obey above relation are known as NEWTONIAN** **fluids and fluids which do not obey the above relation are called NON-NEWTONIAN fluids.

**NEWTONIAN FLUID: **Fluids which obey NEWTONS LAW OF VISCOSITY are known as **NEWTONIAN **fluids.

**NON-NEWTONIAN ****FLUID: **Fluids which do not obey NEWTONS LAW OF VISCOSITY are known as **NON-NEWTONIAN**** **fluids.

## UNITS OF VISCOSITY

The units of viscosity is obtained by putting the dimensions of the quantities in equation

**In MKS System** Force is represented by (Kg f) and Length by meters (m)

**In CGS System** Force is represented by dyne and length by cm and

**In SI System** Force is represented by Newton (N) and Length by meter (m)