Bernoulli’s theorem is applicable only for ________.

CONCEPT:

• Bernoulli's principle: For a streamlined flow of an ideal liquid in a varying cross-section tube the total energy per unit volume remains constant throughout the fluid.
• This means that in steady flow the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline.

• From Bernoulli's principle

\(\frac{{{{\rm{P}}_1}}}{{\rm{\rho }}} + {\rm{g}}{{\rm{h}}_1} + \frac{1}{2}{\rm{v}}_1^2 = \frac{{{{\rm{P}}_2}}}{{\rm{\rho }}} + {\rm{g}}{{\rm{h}}_2} + \frac{1}{2}{\rm{v}}_2^2\)

\(\frac{{\rm{P}}}{{\rm{\rho }}} + {\rm{gh}} + \frac{1}{2}{{\rm{v}}^2} = {\bf{constant}}\)

EXPLANATION:

• In fluid dynamics, Bernoulli’s theorem gives the relation among the elevation, velocity, and pressure in a moving fluid, for which, the viscosity and compressibility are negligible and the flow is laminar or steady.
• Thus the theorem is applicable for incompressible flows. So option 4 is correct.