SIGMA INSTITUTE OF ENGINEERING

Sub : Fluid Mechanics Topic :Fluid Dynamics Group - A Prepared by: Krishna Chauhan-130500106008 Khushbu Patel-130500106032 Sherril Parmar-130500106047 Maitry Purohit-140503106018

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

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

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

Euler’s Equation of Motion

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

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.

Bernoulli’s Equation

Integrating Euler equation For steady flow For steady incompressible flow,

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.

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.

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

Venturimeter

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.

Orifice meter

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

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

Linear momentum equation

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.

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.

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