Bernoulli’s Theorem

Bernoulli’s Theorem and Its Applications

Bernoulli’s theorem which is also called Bernoulli’s principle, states that a rise within the speed of moving air or a flowing fluid is accompanied by a decrease in the air or fluid’s pressure or sum of the kinetic (velocity head), pressure (static head) and Potential energy of the fluid at any point remains constant, provided that the flow is steady, rotational, and frictionless and the fluid is incompressible.

Application of Bernoulli’s theorem

There are 4 common applications of Bernoulli’s theorem.

  • Lift of an aircraft wing
  • Blowing of roofs
  • Bunsen burner
  • Motion of two parallel boats

Lift of an aircraft wing

A section of an aircraft wing and the flow lines are shown in Fig. The orientation of the wing relative to the flow direction causes the flow lines to the crowd together above the wing. This corresponds to increased velocity in this region and hence the pressure is reduced. But below the wing, the pressure is nearly equal to the atmospheric pressure. As a result of this, the upward force on the underside of the wing is greater than the downward force on the topside. Thus there’s a net upward force or raise.

Blowing of roofs

During a storm, the roofs of huts or tinned roofs are blown off without any damage to other parts of the hut. The blowing wind creates a low-pressure P1 on top of the roof. The pressure P2 underneath the roof is but larger than P1. Due to this pressure difference, the roof is lifted and blown off with the wind.

Bunsen burner

In a Bunsen burner, the gas comes out of the nozzle with high velocity. Due to this, the pressure within the stem of the burner decreases. So, air from the atmosphere starts rushing into the burner.

Motion of two parallel boats

Bernoulli’s theorem is also the conducting theory behind sailing. When two boats separated by a small distance row parallel to each other along the same direction, the velocity of water between the boats becomes very large compared to that on the outer sides. Because of this, the pressure in between the two boats gets reduced. The high pressure on the outer side pushes the boats inwards. As a result of this, the boats come closer and may even collide. If the speed of air increases, there is less pressure on keel but higher in speed.

 

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