Euler's equation is a fundamental equation in fluid dynamics that represents the momentum equation for an inviscid flow. It is derived from the application of Newton's second law to a fluid element. Euler's equation relates the changes in velocity and pressure along a streamline in a flow field.

Euler's equation can be written as:

\(\frac{D\mathbf{V}}{Dt} = - \frac{1}{\rho}\nabla P\)

where:
- \(\frac{D\mathbf{V}}{Dt}\) represents the material derivative of velocity, which accounts for both the convective and the local acceleration of the fluid element.
- \(\rho\) is the density of the fluid.
- \(\nabla P\) is the pressure gradient, which represents the change in pressure with respect to position in the flow field.

Explanation of the options:

a) Energy per unit weight: Euler's equation does not directly represent energy per unit weight. Energy per unit weight is typically represented by the Bernoulli equation, which is derived from Euler's equation under certain assumptions.

b) Unsteady flow equation: Euler's equation can be applied to both steady and unsteady flow situations. It represents the momentum equation for the fluid element, regardless of whether the flow is steady or unsteady.

c) Momentum equation: This is the correct answer. Euler's equation represents the momentum equation for an inviscid flow. It relates the changes in velocity and pressure along a streamline in the flow field.

d) Specific energy: Euler's equation does not directly represent specific energy. Specific energy is a measure of the energy per unit mass of a fluid particle and is typically represented by the Bernoulli equation.

In summary, Euler's equation represents the momentum equation for an inviscid flow, relating the changes in velocity and pressure along a streamline. It is a fundamental equation in fluid dynamics and can be applied to both steady and unsteady flow situations.