Total mechanical energy

Although the term static pressure is generally used in designing fen and duct systems and is the performance quoted hy fen manufacturers in tables and charts, the total pressure of the system is a characteristic for which the total mechanical energy must he supplied for the system. Note that when the velocity in a duct remains constant, the velocity head remains constant... 

The surface energy produced by fracture is small when compared with the total mechanical energy stored in the material at the time of fracture, and most of the latter is transformed into heat. This leads to the crushing efficiencies to be low and results show them range between 0.1 and 2%. 

In isolation, the total mechanical energy of a molecule is the sum of three quantised terms that are related to the rotational energy, vibrational energy, and electronic energy ... 

The impact of a UV/Visible photon on an isolated molecule modifies the term ciec in equation (11.1), determining the quantification and variation of its total mechanical energy. This electronic perturbation is also accompanied by modification in the terms rot and vib that correspond to the transition. Many such transitions are possible within the same molecule (Fig. 11.2). These transitions are related to the excitation of valence electrons. 

For any given operating conditions involving the flow of a noncompressible fluid through a pipe of constant diameter, the total mechanical-energy balance can be reduced to the following form ... 

The various forms of energy can be related by the total energy balance or the total mechanical-energy balance. On the basis of 1 Ibmt °f fluid flowing under steady conditions, the total energy balance may be written in differential form as... 

The total mechanical-energy balance in differential form is g V dV,... 

Evaluation of the term / vdp in Eq. (4) may be difficult if a compressible fluid is flowing through the system, because the exact path of the compression or expansion is often unknown. For noncompressible fluids, however, the specific volume v remains essentially constant and the integral term reduces simply to v(p2 - Pi). Consequently, the total mechanical-energy balance is especially useful and easy to apply when the flowing fluid can be considered as noncompressible. 

LIQUIDS. For noncompressible fluids, the integrated form of the total mechanical-energy balance reduces to... 

Example 1 Application of the total mechanical-energy balance to noncom-pressible-flow systems. Water at 61°F is pumped from a large reservoir into the top of an overhead tank using standard 2-in.-diameter steel pipe (ID = 2.067 in.). The reservoir and the overhead tank are open to the atmosphere, and the difference in vertical elevation between the water surface in the reservoir and the discharge point at the top of the overhead tank is 70 ft. The length of the pipeline... 

Total mechanical-energy balance between point 1 (surface of water in reservoir) and point 2 (just outside of pipe at discharge point) ... 

From the total mechanical-energy balance, W0 = theoretical mechanical energy necessary from pump = 70 +48.4 = 118.4 ft lbf/lbm. 

GASES. Because of the difficulty that may be encountered in evaluating the exact integral of v dp and dF for compressible fluids, use of the total mechanical-energy balance is not recommended for compressible fluids when large pressure drops are involved. Instead, the total energy balance should be used if the necessary data are available. 

Because the amount of heat exchanged between the surroundings and the system is unknown, the total energy balance cannot be used to solve this problem. However, an approximate result can be obtained from the total mechanical-energy balance. 

Designate point 1 as the entrance to the pump, point 2 as the exit from the pump, and point 3 as the downstream end of the pipe. Under these conditions, the total mechanical-energy balance for the system between points 2 and 3 may be written as follows ... 

M The mechanical energy added by the pump can be determined by making a total mechanical-energy balance between points 1 and 3 ... 

Where E = + is the total mechanical energy. The solid dots in these equations represent vector dot product. The instability is related to... 

Advection is mechanical transport of solutes along with the bulk flux of the water. It is driven by the gradient in the total mechanical energy of the solution, just as the water flux is driven. For most circumstances, this means the gradient in gravitation potential energy. Advec-tive fluxes are simply the product of the water flux from Darcy s law with the solute concentration ... 

At any point in system through which a fluid is flowing, the total mechanical energy can be expressed in terms of potential energy, pressure energy, and kinetic energy. 

The total mechanical energy of unit mass of fluid is therefore... 

For conservative central forces and a defined interaction potential, V(r), we can write a statement for the total mechanical energy for a particle of mass M, a distance r away from a central force F as... 

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