1. SIGMA INSTITUTE OF ENGINEERING

2. Sub : Fluid Mechanics Topic :Fluid Dynamics
Group - A
Prepared by:
Krishna Chauhan
Khushbu Patel
Sherril Parmar
Maitry Purohit

3. Flow of Presentation Introduction Euler’s equation of motion
Bernoulli’s equation
Venturimeter
Orifice meter
Pitot tube
Linear momentum equation
Application of momentum equation
Force exerted by a flowing fluid on a pipe bend

4. Introduction
Fluid dynamics is the branch of fluid mechanics dealing with the behavior of fluid when it is in motion, with reference to the forces responsible for flow.
FLUID DYNAMICS is known as hydrodynamics
For eg;
change in pressure
flow through orifice
impact of jet
water pressure due to bend in pipe line

5. Energy of Fluid in Motion
1) Potential energy : E=W*Z
W=WEIGHT OF LIQUID
Z=HEAD
2) kinetic energy: V²/2g (m)
3) pressure energy: p/w m
Total energy (E):
E=Z+V²/2g+p/w m

6. Euler’s Equation of Motion

7. • Applying Newton’s second law of conservation of linear momentum relation in the flow field

9. Bernoulli’s Equation :
“In steady, ideal flow of an incompressible fluid, the total energy at any point of the fluid is constant.”
The total energy consist of potential energy, kinetic energy and pressure energy.

10. Bernoulli’s Equation

11. Integrating Euler equation
For steady flow
For steady incompressible flow,

12. Basic Assumptions: 1) Fluid is ideal
Basic Assumptions: 1) Fluid is ideal. 2)Fluid is incompressible 3)The flow is continuous and steady. 4)Flow is irrotational. 5)There is no change in the energy of fluid between two section.

13. Limitation of Bernoulli's equation :
The velocity of every liquid particle across any cross section of a pipe is non-uniform.
External force such as pipe friction is acting on the liquid.
There is loss of energy of the liquid particle while flowing in form of heat and shear force.
If the liquid is flowing in a curved pipe, the energy due to centrifugal force should also be taken into account.

14. Practical Applications of Bernoulli’s Equation
Venturimeter
Orifice meter
Pitot tube

15. Venturimeter

16. Components of Venturimeter:
Converging cone: In converging cone area gradually decreases & hence velocity increases.
Throat: It connects the converging cone & diverging cone.
Diverging cone: In diverging cone area gradually increases & hence velocity decreases.

17. Orifice meter

18. An orifice meter is used to measure the discharge in a pipe.
An orifice meter is consists of a plate having a sharp edge circular hole known as an orifice.
The plate is fixed inside a pipe.
Discharge= coefficient of orifice meter * a2v2
There fore
h=liquid head
a1=area of pipe at inlet
a2=area of pipe at outlet

19. Pitot tube
Pitot is an instrument to determine the velocity of flow at the required point in a pipe or a stream.

20. Linear momentum equation

21. Application of momentum equation:
Flow through pipe bends
Force exerted by a fluid jet striking against fixed or moving vanes.
Jet propulsion
Force on propeller blades
Non-uniform flow through suddenly enlarged pipes.
Hydraulic jump in open channels.

22. Force exerted by a flowing fluid on a pipe bend:
The impulse momentum equation
is used to determine the resultant force exerted by a flowing fluid on a pipe bend.

23. THANK YOU