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FLUID DYNAMICS

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Title: FLUID DYNAMICS


1
FLUID DYNAMICS
  • BERNOULLIS EQUATION
  • BY
  • GP CAPT NC CHATTOPADHYAY

2
Daniel Bernoulli
  • (Groningen, 8 February 1700 Basel, 8 March
    1782) was a Dutch-Swiss mathematician and was one
    of the many prominent mathematicians in the
    Bernoulli family. He is particularly remembered
    for his applications of mathematics to mechanics,
    especially fluid mechanics, and for his
    pioneering work in probability and statistics.
    Bernoulli's work is still studied at length by
    many schools of science throughout the world.

3
INTRODUCTION
  • A statement of the conservation of energy in a
    form useful for solving problems involving
    fluids.
  • For a non-viscous, incompressible fluid in
    steady flow, the sum of pressure, potential and
    kinetic energies per unit volume is constant at
    any point
  • A special form of the Eulers equation derived
    along a fluid flow streamline is often called the
    Bernoulli Equation

4
AVAILABLE ENERGY HEADS
  • 1. PR HEAD DUE TO PR OF LIQUID p/w
  • 2. PE HEAD DUE TO POSITION OF FLUID
    LEVEL z
  • 3. VELOCITY HEAD DUE TO VELOCITY i.e
    KINETIC ENERGY HEAD
    v2/2g

5
STATEMENT
  • FOR A STEADY,STREAMLINE FLOW OF AN IDEAL,
    INCOMRESSIBLE FLUID, THE SUM OF KINETIC,
    POTENTIAL AND PR ENERGY IS CONSTANT

6
EXPLAINATION
SECTION-1
SECTION-2
?1,A1,v1, p1,z1
?2,A2,v2 p2,z2
FLOW
p1 /w v12/2g z1 p2/w v22/2g z2
7
DERIVATION
  • AS DERIVED IN THE CLASS
  • ALSO, PL REFER TO RECOMMENDED TEXT BOOKS

8
NUMERICALS
  • 1. DIA OF A PIPE CHANGES FROM 200mm AT A SECTION
    5m ABOVE DATUM TO 50mM AT A SECTION 3m ABOVE
    DATUM. PRESSURE OF WATER IS 500kPa AT INLET WITH
    A VELOCITY 1m/s. DETERMINE PR AND VELOCITY AT
    EXIT.
  • 2. BRINE OF S.G 1.15 IS DRAINING FROM BOTTOM OF A
    LARGE OPEN TANK. THE DRAIN PIPE ENDS 10 m BELOW
    THE FREE SURFACE. CONSIDERING THE FLOW AS STEADY
    AND ALONG STREAMLINE CALCULATE THE DISCHARGE
    VELOCITY. (NEGLECT FRICTION)

9
ASSIGNMENT
  • 1. PRACTISE DERIVATION OF BERNOULLIS EQUATION
  • 2. SOLVE.
  • A 5m LONG PIPE IS INCLINED AT 150 TO THE
    HORIZONTAL. SMALLER END OF PIPE IS AT LOWER LEVEL
    AND IS OF 80mm DIA WHILE THE LARGER SECTION IS OF
    240mm DIA. IF THE INLET VELOCITY IS 1m/S, FIND
    EXIT VELOCITY AND PR DIFFERENCE BETWEEN TWO
    SECTIONS

10
EULERS EQUATION OF MOTION
  • AS DERIVED ON THE BOARD
  • BERNOULLIS EQUATION WILL BE ESTABLISHED FROM
    ABOVE

11
ASSUMPTIONS
  • FLOW IS STEADY
  • FLOW IS INCOMPRESSIBLE
  • FLOW IS ALONG STREAMLINE (1 D)
  • FLOW IS INVISID
  • NO HEAT OR WORK TRANSFER
  • NO ENERGY LOSS TO ENVIRONMENT
  • VELOCITY IS UNIFORM (Um)
  • ONLY FORCES ARE DUE TO PR AND GRAVITY

12
LIMITATIONS
  • VELOCITY MAY NOT BE UNIFORM IN A REAL FLOW
  • VISCOUS AND FRICTIONAL FORCES EXIST IN A REAL
    FLOW
  • CENTRIFUGAL FORCE MAY ALSO BE PRESENT IN A FLOW
    THROUGH CURVED PATH
  • HEAT TRANSFER ALSO OCURS DUE TO CONVERSION OF
    KINETIC ENERGY INTO HEAT

13
Application of Bernoullis Principle
14
MAJOR APPLICATIONS
  • MEASUREMENT OF FLOW VELOCITY
  • MEASUREMENT OF FLOW DISCHARGE

15
PITOT TUBE (WITH AOAI)
16
PITOT TUBE
Stagnation pressure static pressure dynamic
pressure Which can also be written
                   Solving that for velocity we
get                   
17
USE OF PITOT SYSTEM
18
PITOT STATIC SYSTEM
19
DISCHARGE MEASUREMENT
  • VENTURIMETER
  • ORIFICEMETER
  • ROTAMETER

20
VENTURIMETER
A venturi can be used to measure the volumetric
flow rate Q. Since
then
21
ORIFICE METER
22
ROTAMETER
A rotameter is a device that measures the flow
rate of liquid or gas in a closed tube. It
belongs to a class of meters called variable area
meters, which measure flow rate by allowing the
cross-sectional area the fluid travels through to
vary, causing some measurable effect.
23
SO,WHAT DO U DO ?
  • CONCENTRATE ON THE BOARD FOR THE DERIVATION
  • GO THROUGH THE TOPIC COVERED SO FAR AND
  • HAVE PATIENCE TILL NEXT FM CLASS
  • ON THE BOARD PL..

24
TIME TO ENJOY.
EID MUBARK. SEE U ALL ON THE FIRST DAY FIRST
SHOW. AFTER BREAK..
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