Bernoulli’s Principle and Equation

During 17th century, Daniel Bernoulli investigated the forces present in a moving fluid, derived an equation and named it as an Bernoulli’s equation. Below image shows one of many forms of Bernoulli’s equation.
The Bernoulli equation gives an approximate equation that is valid only in inviscid regions of flow where net viscous forces are negligibly small compared to inertial, gravitational or pressure forces. Such regions occur outside of boundary layers and waves.
Bernoulli's Principle

Image Source: Hyperphysics

Despite its simplicity, Bernoulli’s Principle has proven to be a very powerful tool in fluid mechanics.
Care must be taken when applying the Bernoulli equation since it is an approximation that applies only to inviscid regions of flow. In general, frictional effects are always important very close to solid walls and directly downstream of bodies.
The motion of a particle and the path it follows are described by the velocity vector as a function of time and space coordinates and the initial position of the particle. When the flow is steady, all particles that pass through the same point follow the same path and the velocity vectors remain tangent to the path at every point.

Assumptions in Bernoulli’s equation:

  • Fluid is ideal and incompressible.
  • Flow is steady
  • Flow is continuous
  • Flow is non-viscous
  • Flow is irrotational
  • Applicable along a stream line.

Vinodh Reddy is an Editor-in-chief of ME Mechanical. He holds Bachelor of Engineering (Honours) degree in Mechanical Engineering from BITS-Pilani. He also writes for vrcworks.net and EduGeneral.

All Comments

  • The presentation of ME subject articles by you has created interest once again after leaving my Engineering college after 48 years,after seeing the FB postings by some on Electrical Engineering subject recently.I forget almost every thing at this age,but your simple presentation of the well known Bernoulli’s theorem makes me to recollect my olden days once again.Now the students and faculty members are very lucky to have computers,and other devices to learn any subject unlike in olden days.In other way,for the efforts put by students now a days ,final result in examinations will be more than on those days of efforts,provided interest is also of same level in studies.

    canbkrao Dec 7, 2015 3:27 pm Reply
  • nice work

    sinan Feb 23, 2016 8:01 pm Reply
  • very useful website for mechanical’ engineers
    big ups to the founders

    Hillary Turyahebwa May 4, 2016 3:02 am Reply

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