Discuss the different types of energies possessed by a flowing liquid .derive an expression for the title energy per unit mass of a flowing liquid.
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When a liquid flows, it possesses several different types of energies. These energies include kinetic energy, potential energy, and internal energy.
1. Kinetic Energy: Kinetic energy of a flowing liquid is the energy it possesses due to its motion. The kinetic energy per unit mass of a liquid can be calculated using the formula:
Kinetic Energy per unit mass (K.E.) = (1/2) x velocity^2
2. Potential Energy: Potential energy of a flowing liquid is the energy it possesses due to its position or height above a reference point. The potential energy per unit mass of a liquid can be calculated using the formula:
Potential Energy per unit mass (P.E.) = acceleration due to gravity x height
3. Internal Energy: Internal energy of a flowing liquid is the total energy possessed by its molecules, including their microscopic motion, potential energy due to their positions, and the energy associated with intermolecular forces. Calculating the exact internal energy of a flowing liquid usually requires considering its temperature, pressure, and specific characteristics of the liquid.
Now let's derive the expression for the total energy per unit mass, also known as the specific total energy, of a flowing liquid. This expression combines all three types of energies mentioned above.
Total Energy per unit mass = Specific Kinetic Energy + Specific Potential Energy + Specific Internal Energy
Total Energy per unit mass = (1/2) x velocity^2 + acceleration due to gravity x height + Specific Internal Energy
Please note that the specific internal energy calculation depends on the specific properties and characteristics of the liquid being considered, and a detailed analysis of thermodynamics and fluid mechanics is usually required to determine it accurately.