Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Mechanical Engineering SSC JE (Technical)

Mechanical Engineering : Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

The document Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev is a part of the Mechanical Engineering Course Mechanical Engineering SSC JE (Technical).
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FLUID DYNAMICS

  • Reynolds equation  = Intertia force + gravity force + viscous force + turbulence force + pressure force  
  • Navier - Stoke's equation = Intertia gravity force  +  pressure force  +  viscous force 
  • Eulers equation (represents momentum equation in a 2-D, inviscid steady flow) Inertia force = gravity force  +  pressure force  
  • Bernoulli's equation (Conservation of Energy)
    Assumptions in Bernoullis equations:
    (i) fluid is ideal
    (ii) flow is steady
    (iii) flow is continous
    (iv) fluid is incompressible
    (v) flow is non-viscous
    (vi) flow is irrotational
    (vii) applicable along a stream line
    Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

where,

Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev 
= velocity head

Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

= pressure head

z = elevation of datum head

Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

=  piezometric head

Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  • The line representing the sum of all 3 heads is known as total energy line or total head line. 
  • Line joining the points of piezometric heads is known as hydraulic grade line or piezometric line. 
  • Piezometric head remains constant normal to the stream lines in case of uniform diameter straight pipe. 
  • Flow in pipe bend, considered as irrotational flow. Piezometric head line for outer boundary is above than the inner boundary and pressure is also more at outer boundary 
  • HGL is always parallel and lower than TEL.

 

  • Energy gradient

Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  • Hydraulic gradient

Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  • Kinetic Energy correction factor 
    (i) For laminar flow in pipes, a = 2
    (ii) For fully develop turbulent flow in pipes, a = 1.33 Lower value is applicable for rough surface and high Reynolds number. 
  • Pressure at stagnation point where velocity of flow is zero is known as the stagnation pressure.

 Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

where p= static pressure and

 Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
= dynamic pressure

  •  Flow through Pipe bend

 Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

P1A1 – P2A2 cos q +  
Fx = rQ (V2 cos q – V1)
Fy – P2A2 sin q = rQ (V2 sin q – 0)
Fx and Fy represents the reaction of bend on water. 

  • Torque exerted by the water on the pipe will be
    T = rQ1 V1 r1 - rQ2 V2 r2

Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

 V1 = tangential velocity component of absolute velocity at 1
V2 = tangential velocity component of absolute velocity at 2

 Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
Chapter 5 Fluid Dynamics - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

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