RAJIB SAHAKALIN CHAKMASANJIDA IFFATTANNABI MAHTABSHAKIL AHMED

Fluid mechanics and its application

FLUID MECHANICS

The branch of mechanics dealing with the properties of fluids in various states and with their reaction to forces acting upon them

FLUID MECHANICS CAN BE DIVIDED INTO 3 DIVISIONS:

Hydrostatics: that studies the mechanics of fluids at absolute and relative rest.

Kinematics: deals with translation, rotation and deformation of fluid without considering the force and energy causing such a motion.

Dynamics: that prescribes the relation between velocities and acceleration and the forces which are exerted by or upon the moving fluids.

FOR ALL PRACTICAL PURPOSES , THE LIQUIDS AND SOLIDS CAN BE REGARDED AS INCOMPRESSIBLE. THIS MEANS THAT PRESSURE AND TEMPERATURE HAVE PRACTICALLY NO EFFECT ON THEM EG WATER, KEROSENE, PETROL ETC. But Gases are readily compressible

fluids. They expand infinitely in the absence of pressure and contract easily under pressure. Eg air ,ammonia etc.

SIGNIFICANCE OF FLUID MECHANICS Design of wide range of hydraulic structures

(dams,canals) and machinery ( pumps,turbines).

Fluidic control devices; both pneumatic and hydraulic.

Design and analysis of gas turbine , rocket engine, super sonic aircrafts.

Human circulatory system i.e the flow of blood in veins and the pumping action of heart.

IDEAL FLUID: A FLUID IS SAID TO BE IDEAL IF IT IS ASSUMED TO BE BOTH INCOMPRESSIBLE AND IN VISCID (NON-VISCOUS).

Ideal fluid has no surface tension and viscosity is zero and no frictional forces are set up even during the fluid motion.

Ideal Fluids are imaginary and do not exist in nature .

REAL FLUID: PRACTICAL FLUID HAVE SURFACE TENSION, VISCOSITY AND COMPRESSIBILITY.

Whenever motion takes place, the tangential or shear forces always come into play due to viscosity and some frictional work is done.

DENSITY ()Density is the mass of the fluid per unit

volume = m/v Units : Kg/m3

SPECIFIC GRAVITY(S):

The specific gravity is the ratio of the density or specific weight of the fluid to the density or specific weight of water,

at a temperature of 4oC

For Gases the standard fluid is taken either air at 00 C or Hydrogen at the

same temperature.

IT IS DIMENSIONLESS QUANTITY.

A Statement that the specific gravity of mercury is 13.6 implies that its weight (or mass) in 13.6 times that of the same volume of water.

In simple words, mercury is 13.6 times heavier than water.

SPECIFIC VOLUME: REPRESENTS THE VOLUME PER UNIT MASS OF FLUID.

Specific Volume is the inverse of the mass density.

v= V/m or v=1/ The concept of specific volume is found

to be more useful in the study of flow of compressible fluids i.e gases.

VISCOSITY: IT IS THE PROPERTY OF THE FLUID BY VIRUE OF WHICH IT OFFERS RESISTANCE TO SHEAR OR ANGULAR DEFORMATION.

Mollases,tar, glycerine are highly viscous fluids.

Water,air,petrol have very small viscosity and are called thin fluids.

NEWTON’S LAW OF VISCOSITY = (du/dy)

Where, du/dy =velocity gradient = coefficient of viscosity, absolute

viscosity or dynamic viscosity.

FOLLOWING OBSERVATIONS CAN BE MADE FROM NEWTON’S VISCOSITY EQUATION:

Max. shear stress occur when velocity gradient is largest and shear stress disappears where velocity gradient is zero.

Velocity Gradient becomes small with distance from the boundary.Consequently the max value of shear stress occurs at the boundary and it decreases from the boundary.

BERNOULLI’S EQUATION

In steady flow of a non viscous, incompressible fluid, the pressure, the

fluid speed, and the elevation at two points are related by:

PUMPS: It is a steady-state, steady-flow machine in which mechanical work is added to the fluid in order to transport the liquid from one point to another point of higher pressure.

LowerReservoir

Upper Reservoir

Suction GaugeDischarge Gauge

Gate Valve

Gate Valve

FUNDAMENTAL EQUATIONS

1. TOTAL DYNAMIC HEAD

meters HZZ2g

vvPPH L12

2

1

2

212t

γ

2. DISCHARGE or CAPACITY Q = Asvs = Advd m3/sec

3. WATER POWER or FLUID POWER WP = QHt KW

4. BRAKE or SHAFT POWER

KW 60,000

TN2BP

π

HYDRO ELECTRIC POWER PLANTA. Impulse Type turbine (Pelton Type)

Headrace

Tailrace

Y – Gross HeadPenstock turbine

1

2

B. Reaction Type turbine (Francis Type)

Headrace

Tailrace

Y – Gross HeadPenstock

ZB

1

2Draft Tube

B

Generator

B – turbine inlet

REFERENCE:

1: wikipedia 2: fluid mechanics by FRANK M.WHITE