Bernoulli's equation for steady, frictionless, continuous flow states that the __________ at all sections is same.

ANS:B - total energy

Bernoulli's equation for steady, frictionless, continuous flow states that the total energy at all sections is the same. Here's an explanation: Bernoulli's equation is an expression of the conservation of energy for flowing fluids under certain idealized conditions:

• Steady Flow: The fluid flow does not change with time at any point in the fluid.
• Frictionless Flow: There are no energy losses due to viscosity or friction between fluid layers.
• Continuous Flow: The fluid is incompressible and flows continuously along streamlines.

The equation states that the total mechanical energy per unit mass (which includes potential energy due to height, kinetic energy due to velocity, and pressure energy) remains constant along a streamline: Pρ+v22+gz=constant\frac{P}{\rho} + \frac{v^2}{2} + gz = \text{constant}ρP​+2v2​+gz=constant where:

• PPP is the static pressure of the fluid,
• ρ\rhoρ is the density of the fluid,
• vvv is the velocity of the fluid,
• ggg is the acceleration due to gravity,
• zzz is the height above a reference plane.

This equation implies that the total energy (sum of pressure energy, kinetic energy, and potential energy per unit mass) is conserved along a streamline in the flow field. Therefore, in the context of Bernoulli's equation:

• Total Energy at all sections along a streamline remains the same.

Hence, the correct statement is that Bernoulli's equation states that the total energy at all sections is the same.