Fluid Dynamics | Mechanical Engineering SSC JE (Technical)

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
  

where,

 
= velocity head

= pressure head

z = elevation of datum head

=  piezometric head

• 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

• Hydraulic gradient

• 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.

where p_o = static pressure and

 
= dynamic pressure

•  Flow through Pipe bend

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

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

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