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## FLUID DYNAMICS

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Title: FLUID DYNAMICS

1
FLUID DYNAMICS
• BERNOULLIS EQUATION
• BY

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
• 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
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 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..