Energy friction neglected

Note that frictional dissipation and pressure energy are neglected. 

This relative flow is the flow as it would appear to an observer or a camera revolving with the vessel. The pressure difference due to this superimposed flow alone is found by the energy equation, neglecting friction losses, to be (p2/w) - (pjw) = (uf - u /2g. Hence for the case of rotation with flow, the total pressure difference between two points is found by adding together the pressure differences due to the two flows considered separately. That is ... 

If we scale time as t = xr, then the frst term in (5.52) decreases as l/>/, while the other two are independent of friction. Therefore, at large rj the second derivative term in (5.52), as well as the kinetic energy term in the action, can be neglected, and the entire effect of friction is to change the timescale. That is, the solution to (5.52) is Q x) = Q x/ri) where Q is a function independent of rj. The instanton velocity is scaled as Q cc and the action (5.38) grows linearly with r, ... 

Here a is the elastic stress which arises from the change in the (dynamic) free energy in the macroscopic flow, while o(V) and a(S) are the viscous stresses produced by the polymer-solvent friction and the solvent-solvent friction, respectively. In concentrated isotropic polymer solutions, the elastic stress overwhelms the viscous stresses, so the latter are often neglected. However, it should be noticed that the viscous stresses may become significant in more dilute solutions as well as in nematic solutions where the elastic stress diminishes. 

When elevation head and work transfer are neglected, the mechanical energy balance equation (6.13) with the friction term of Eq. (6.18) become... 

For the gas flow in a riser, energy in the gas phase is partially transferred into the solids phase through gas-particle interactions and is partially dissipated as a result of friction. Under most operating conditions, gravitational effects dominate overall gas phase energy consumption. Thus, neglecting the particle acceleration effects, the pressure drop in the... 

Jet trajectory. A free liquid jet in air will describe a trajectory, or path under the action of gravity, with a vertical velocity component which is continually changing. The trajectory is a streamline consequently, if air friction is neglected, Bernoulli s theorem may be applied to it, with all the pressure terms 0. Thus, the sum of the elevation and velocity head must be the same for all points of the curve. The energy gradient is a horizontal line at distance V2/2g above the nozzle, where V is the velocity leaving the nozzle. 

Consider a solitary wave, progressing to the left in an open channel, with celerity (wave velocity) c. We may replace this situation with the equivalent steady-flow case in which the wave stands still while the flow enters at velocity Vi = -c. Writing the energy equation, Eq. (10.122), between points 1 and 2 (with Z = z2, oq = a2 = 1, and neglecting friction), and keeping the same variable definitions, we have... 

The reactor is modeled by three partial differential equations component balances on A and B [Eqs. (6.1) and (6.2)] and an energy balance [Eq. (6.3) for an adiabatic reactor or Eq. (6.4) for a cooled reactor]. The overall heat transfer coefficient U in the cooled reactor in Eq. (6.4) is calculated by Eq. (6.5) and is a function of Reynolds number Re, Eq. (6.6). Equation (6.7) is used for pressure drop in the reactor using the friction factor /given in Eq. (6.8). The dynamics of the momentum balance in the reactor are neglected because they are much faster than the composition and temperature dynamics. A constant... 

Figure 9 The normalized vibrational friction felt by a range of diatomic solutes dissolved in liquid carbon dioxide and liquid acetonitrile (62). The solutes are meant to represent the nondipolar molecule Br2 itself and two bromine mimics differing only in the replacement of the bromine quadrupole by permanent dipoles of different strengths. The d5 solute has a dipole moment of 5.476 D and the d8 solute a dipole moment of 8.762 D. (The notation r/vv emphasizes the fact that only potential-energy contributions are included in the calculations centrifugal force terms are neglected.)...

Interphase transfer kinetics. At this point, we need to characterize the process that leads to the transfer of the property through the interphase. The transport of the momentum from one phase to another is spectacular when the contacting phases are deformable. Sometimes in these situations we can neglect the friction and the momentum transfer generates the formation of bubbles, drops, jets, etc. The characterization of these flow cases requires some additions to the momentum equations and energy transfer equations. 

Given fluid conditions (pressure, flow rate, velocity, elevation) at the inlet and outlet of an open system and values of friction loss and shaft work within the system, substitute known quantities into the mechanical energy balance (or the Bernoulli equation if friction loss and shaft work can be neglected) and solve the equation for whichever variable is unknown. 

This derivation neglects the correction of kinetic energy loss due to nonuniformity of flow in both cross sections and the frictional degradation of energy during passage through the constriction. This is corrected by the introduction of a numerical coefficient, Cd ... 

This amount of energy could have been recovered, neglecting friction and other losses, or used to drive the vehicle up a hill. 

---