Question

Explain with sketch the limitation on the use of Bernoulli equation؟

Answer 1

bernoullis qeuation

V2 + + z = constant on a streamline 28 у

• The basic restriction on use of the Bernoulli equation is that there are no mechanical devices (pumps or turbines) in the system between the two points along the streamline for which the equation is applied.
• 
  chund
  in the above figure we cannot apply bernoullis equation betwwen 1 and 2 as pump is involved
• Another restriction of the Bernoulli equation is the assumption that the flow is steady. For such flows, on a given streamline the velocity is a function of only the location along the streamline. For unsteady flows the velocity is also a function of time.
• 
  Н 0 2
  in the above figure head of the tank H is not constant as the tank empties H value varies with time, so it is not steady so we cannot apply bernoullies equation
• The main assumptions in deriving the Bernoulli equation is that the fluid is incompressible. Although this is reasonable for most liquid flows, it can, in certain instances, introduce considerable errors for gases. A rule of thumb is that the flow of a perfect gas may be considered as incompressible provided the Mach number is less than about 0.3. so even in liquids if the velocity is high then bernoullies equation is not valid.
• Another restriction on the Bernoulli equation is that the flow is inviscid.If viscous effects are important, the system is nonconservative and energy losses occurs. these losses appear as headloss(h_L) in energy equation ie
• 
  V2 in Pout 7 + out 28 + Zout Pin у + V? + Zin th, he 2g