It states that the sum of pressure energy per unit volume (P), the kinetic energy per unit volume (rv2/2) and the potential energy per unit volume (rgh) of an ideal fluid remain constant along the stream line. i.e.
where Pis pressure, r is density, v is velocity and h is the height above datum of the point in stream line.
This is a mathematical expression for the conservation of energy in fluid flow. If energy is defined in terms of per unit mass or per unit weight then Bernouli’s equation can be written as
[per unit mass]
[per unit weight)
where and hare called velocity, pressure and potential head respectively.
In case of flowing fluid, pressure cannot be obtained by applying Pascal's is law rather it can only be obtained by applying Bernoulli equation.
(i) Drop of pressure when fluid moves from broader to narrower horizontal pipe:
According to continuity equation Av = constant
So, where the area is small, velocity will be large and vice-versa.
But by Bernoulli's equation for a horizontal pipe (i.e. h= constant)
P +(l/2)rv2 = constant
i.e. where the velocity is large, pressure will be small. Hence, when fluid flows from broader to narrower pipe, its velocity increases and so the pressure decreases.
(ii) Blowing off the roots by wind storms: During a tornado when a high speed wind blows over a roof of straw or tin, it creates a low pressure in accordance with Bernoulli's theorem. However pressure below the roof is still atmospheric. So due to this difference of pressure, the roof is lifted up and is then blown off by the wind.
(iii) Attraction between two closely parallel moving boats or buses: When two boats or buses move side by side in the same direction, the water (or air) in the region between them moves faster than that on the remote sides. Consequently in accordance with Bernoulli’s principle, the pressure between them is reduced and hence due to pressure difference they are pulled towards each other creating the so called attraction.
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