Energy Fanning equation

The second term in the mechanical-energy balance. Equation 5.1, is the change in potential energy and requires no comment. The third term is "pressme work" and its evaluation depends on whether the fluid is compressible or incompressible. Because the increase in pressure across the fan is small, we treat the flow as essentially incompressible. Thus, the fluid density may be removed from the integral sign and the mechanical energy balance becomes... 

The frictional effects of bends and fittings are often expressed in terms of a quantity called the velocity head drop . To introduce this concept, we begin by observing that the specific energy lost to friction, F(J/kg), for incompressible flow follows from an integration of the Fanning equation (4.20) with friction factor and velocity constant over the length of pipe ... 

We begin by observing that the energy lost to friction is found by integrating the Fanning equation (4.20), repeated below ... 

Frictional losses in mechanical-energy-balance equation. The frictional losses from the friction in the straight pipe (Fanning friction), enlargement losses, contraction losses, and losses in fittings and valves are all incorporated in the F term of Eq. (2.7-28) for the mechanical-energy balance, so that... 

Head. The tme meaning of the total developed pump head, H, is the amount of energy received by the unit of mass per unit of time (14). This concept is traceable to compressors and fans, where engineers operate with enthalpy, a close relation to the concept of total energy. However, because of the almost incompressible nature of Hquids, a simplification is possible to reduce enthalpy to a simpler form, a Bernoulli equation, as shown in equations 1—3, where g is the gravitational constant, SG is specific gravity, y is the density equivalent, is suction head, is discharge head, and H is the pump head, ie, the difference between H, and H. 

Numerous researchers have studied damage to micro-organisms during flow in pipes, (Fig. 11) [87,88] Most researchers use a Fanning friction factor, f, to calculate the energy dissipation rate for fully developed flow in tubular bioreactors and capillary flow devices. There are minor differences in the equations that are used but they are generally of the following form [89,901 ... 

The mass flows include fuel (F), oxygen (O2), liquid water (1), evaporated water vapor (g) and forced flows (fan). The chemical energy or firepower is designated as Q and all of the heat loss rates by q. While Figure 12.4 does not necessarily represent a fire in a room, the heat loss formulations of Chapter 11 apply. From Equation (3.48), the functional form of the energy equation is... 

The CRE approach for modeling chemical reactors is based on mole and energy balances, chemical rate laws, and idealized flow models.2 The latter are usually constructed (Wen and Fan 1975) using some combination of plug-flow reactors (PFRs) and continuous-stirred-tank reactors (CSTRs). (We review both types of reactors below.) The CRE approach thus avoids solving a detailed flow model based on the momentum balance equation. However, this simplification comes at the cost of introducing unknown model parameters to describe the flow rates between various sub-regions inside the reactor. The choice of a particular model is far from unique,3 but can result in very different predictions for product yields with complex chemistry. 

Equation (5.52) is Bernoulli s theorem [16], an energy equation that is well known to be equal to the sum of the elevation head, the pressure head, and the velocity head. Here the elevation head has been left out because the fan suction air pressure and the exiting air pressure from the air cooler are both equal. 

The DPAT variable is found by applying Eq. (5.48), the static pressure loss per tube row, a key equation that is to be experimentally determined. The last term, u2/2g, is the velocity head energy of the fan required to move the required airflow through the air cooler. As the air is heated while passing through the fin tubes, it expands, causing an increase in velocity. The air velocity difference, (v2 - iq)2, is the velocity head in the Bernoulli equation. 

In turbulent flow the frictional pressure drop down the drill pipe must be calculated from equations that have been determined empirically. The commonest method in drilling fluid hydraulics (91-93) is to use a friction factor/, the so-called Fanning friction factor, defined by the ratio of the wall shear stress rw to the kinetic energy per unit volume of the flowing fluid 0.5 pvm2 (94)... 

In the process of calculation, determine flow field whether arrive at convergence according turbulent kinetic energy, turbulence dissipation rate, velocity and residual of continuity equation (Han, Z.Z et al. 2004, Fan, J.R et al. 2001). Suppose residual of the above physical quantity is 1.0 x 10" , flow field arrive at convergence in this numerical simulation. 

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