FLUID DYNAMICS

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FLUID DYNAMICS

• BERNOULLIS EQUATION
• BY
• GP CAPT NC CHATTOPADHYAY

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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.

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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

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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

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STATEMENT

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

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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
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DERIVATION

• AS DERIVED IN THE CLASS
• ALSO, PL REFER TO RECOMMENDED TEXT BOOKS

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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)

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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

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EULERS EQUATION OF MOTION

• AS DERIVED ON THE BOARD
• BERNOULLIS EQUATION WILL BE ESTABLISHED FROM
  ABOVE

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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

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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

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Application of Bernoullis Principle
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MAJOR APPLICATIONS

• MEASUREMENT OF FLOW VELOCITY
• MEASUREMENT OF FLOW DISCHARGE

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PITOT TUBE (WITH AOAI)
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PITOT TUBE
Stagnation pressure static pressure dynamic
pressure Which can also be written
                   Solving that for velocity we
get                   
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USE OF PITOT SYSTEM
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PITOT STATIC SYSTEM
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DISCHARGE MEASUREMENT

• VENTURIMETER
• ORIFICEMETER
• ROTAMETER

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VENTURIMETER
A venturi can be used to measure the volumetric
flow rate Q. Since
then
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ORIFICE METER
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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.
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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..

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