Bernoulli's Equation In Irrotational Flow we have obtained Bernoulli’s equation This equation was obtained by integrating the Euler’s equation (the equation of motion) with respect to a displacement ' ds' along a streamline. Thus, the value of C in the above equation is constant only along a streamline and should essentially vary from streamline to streamline. The equation can be used to define relation between flow variables at point B on the streamline and at point A, along the same streamline. So, in order to apply this equation, one should have knowledge of velocity field beforehand. This is one of the limitations of application of Bernoulli's equation. Irrotationality of flow field Under some special condition, the constant C becomes invariant from streamline to streamline and the Bernoulli’s equation is applicable with same value of C to the entire flow field. The typical condition is the irrotationality of flow field. Proof: Let u...
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