Euler's equation is given as dp=−ρvdv
This equation applies to an incompressible and in-viscid flow where ρ=constant. In a streamline, in between two points 1 and 2, the above Euler equation can be integrated as p2∫p1dp=−ρv2∫v1vdv
p2−p1=−ρ(v222−v212)
⇒p1+12ρv21=p2+12ρv22
This can be written asp+12ρv2=constant
for a streamline.For an rotational flow the value of constant is changing from streamline to another.For irrotational flow,the constant is same for all streamlines and p+12ρv2=constant
throughout the flow. Physical significance of Bernoulli's equation is that when the velocity increases, the pressure decreases and when the velocity decreases, the pressure increases. ...