Question

Which one of the following statements about the energy equation (2.20) is correct?

a) It is valid for both compressible and incompressible flow.
b) It is valid only if the flow is steady state.
c) It is valid for viscous flow.
d) It is valid when shaft work is present.

Answer 1

Bernoulli's equation is valid for both compressible and incompressible flows but should be used with caution for compressible flows as it assumes incompressibility and non-viscous, steady-state conditions. (option a)

Step-by-step explanation:

The energy equation (2.20) mentioned is most likely referencing a form of the conservation of energy in fluid dynamics, such as Bernoulli's equation. To address the student's question regarding which statement about the energy equation is correct, we should consider several principles.

First, Bernoulli's equation is valid for incompressible flow, typically applied to essentially incompressible liquids. Since gases are compressible, Bernoulli's equation must be applied with caution to gases under compression or expansion. Secondly, the equation is typically used in the context of steady-state flow where the flow properties at any given point do not change over time.

Third, Bernoulli's equation assumes non-viscous (frictionless) flow, though there are more complex versions for viscous flow that involve additional terms. Lastly, the equation can incorporate the effects of shaft work or external work done by or on the fluid.

The correct statement about the energy equation in fluid dynamics is: (a) It is valid for both compressible and incompressible flow, though caution must be exercised for compressible flows.