Bernoulli's equation for fluid flow is derived following certain assumptions. Out of the assumptions listed below, which set of assumptions is used in derivation of Bernoulli's equation ?
A. Fluid flow is frictionless & irrotational.
B. Fluid flow is steady.
C. Fluid flow is uniform & turbulent.
D. Fluid is compressible.
E. Fluid is incompressible.

ANS:C - A, B, E

Bernoulli's equation for fluid flow is derived based on certain assumptions that simplify the analysis of fluid dynamics. Let's analyze each option: A. Fluid flow is frictionless & irrotational.

• Frictionless: This assumption implies that there is no viscous drag or energy loss due to friction between fluid layers.
• Irrotational: This assumption means that the fluid does not have any rotational motion about its center of mass. This simplifies the flow field to be described mainly by its velocity potential.

B. Fluid flow is steady.

• This assumption states that the flow parameters (velocity, pressure, density) do not change with time at any point in the fluid.

C. Fluid flow is uniform & turbulent.

• Uniform: This would imply that the flow velocity is constant at every point in the fluid, which is typically not assumed in Bernoulli's equation derivation.
• Turbulent: Turbulent flow involves chaotic, irregular fluctuations in velocity and pressure, which are not assumed in the derivation of Bernoulli's equation.

D. Fluid is compressible.

• If the fluid is compressible, its density can change due to pressure variations, which complicates the application of Bernoulli's equation, designed for incompressible flows.

E. Fluid is incompressible.

• Incompressible flow assumes that the density of the fluid remains constant, simplifying the continuity equation and the application of Bernoulli's equation.

Now, let's determine which assumptions are typically used in the derivation of Bernoulli's equation:

• A. Fluid flow is frictionless & irrotational. This assumption simplifies the energy conservation along streamlines.
• B. Fluid flow is steady. This ensures that the flow parameters remain constant with respect to time.
• E. Fluid is incompressible. This simplifies the continuity equation and is commonly assumed for incompressible flows.

Therefore, the correct set of assumptions used in the derivation of Bernoulli's equation is: A, B, E These assumptions together allow for the derivation of Bernoulli's equation, which relates the pressure, velocity, and elevation of a fluid along a streamline under steady flow conditions, assuming the fluid is incompressible, frictionless, and irrotational.