Discuss the different types of energies possessed by a flowing liquid. Derive an expression for the total energy per unit mass of a flowing liquid

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When a liquid flows, it possesses different types of energies. These can be classified into three main types: potential energy, kinetic energy, and internal energy.

1. Potential Energy: This is the energy associated with the position of a liquid in a gravitational field. The potential energy per unit mass can be obtained by multiplying the height (h) of the liquid above a reference point by the acceleration due to gravity (g). This is given by the equation P = h * g.

2. Kinetic Energy: This is the energy associated with the motion of the liquid. The kinetic energy per unit mass can be calculated using the equation K = (1/2) * V^2, where V is the velocity of the liquid.

3. Internal Energy: This is the energy associated with the internal molecular motion and interaction of the liquid. It includes the microscopic energies of the liquid such as molecular kinetic energy and potential energy due to intermolecular forces.

Now, to derive an expression for the total energy per unit mass of a flowing liquid, we need to consider the sum of potential energy, kinetic energy, and internal energy.

Total energy per unit mass (E) = Potential energy per unit mass (P) + Kinetic energy per unit mass (K) + Internal energy per unit mass (I)

Therefore, E = P + K + I

Substituting the equations derived above, we have:

E = (h * g) + (1/2) * V^2 + I

It is important to note that the internal energy term (I) can be complex and depend on factors like temperature, phase changes, and composition. In many cases, for simplicity, the internal energy term can be approximated or neglected depending on the specific conditions of the flowing liquid.