Subject Name Fluid Mechanics Subject Code 10 ME

Subject Name: Fluid Mechanics Subject Code: 10 ME 36 B Prepared By: PUNITH R Department: AE Date: 22 -08 -2014

UNIT-04 Fluid Dynamics

Fluid Dynamics It is defined as the Study of fluid motion with the forces causing flow. Newton’s second law of motion The net force acting on a fluid element in the direction of x is equal to mass m of the fluid element multiplied by the acceleration in the x-direction. Thus mathematically, Fx=max

Fx=max Where, Fx=(Fg)x+(Fp)x+(Fv)x+(Ft)x+(Fc)x Where, (Fg) = Gravitational force (Fp) = Pressure force (Fv) = Force due to viscosity (Fc) = Force due to Turbulence (Ft) = Force due to compressibility

Assumptions needed for Bernoulli Equation • • The fluid is ideal The fluid is steady The flow is incompressible The flow is irrotational

Bernoulli’s Theorem It states that in a steady, ideal flow of an incompressible fluid. The total energy at any point of the fluid is constant. ρ

Bernoulli Equation ρ ρ Pressure head Piezometric head Elevation head Velocity head Total head

Limitations of Bernoulli’s Theorem • It has been derived under the following assumptions that • Velocity of every liquid particle, across any of pipe is uniform , but in actual practice it is not so. • No external force is present except the gravity force, but in actual practice it is not so. • There is no loss of energy of liquid particle while flowing, but in actual practice it is not so. • If the fluid is flowing in curved path, energy due to centrifugal force should also be taken in to account.

Applications of Bernoulli’s Theorem • • Stagnation tube Pitot tube Free Jets Orifice meter Venturi meter Sluice gate Sharp-crested weir