Turbulent mechanical energy balance

S based on experiments with water in turbulent flow, in channels icient roughness that there is no Reynolds number effect. The hydraulic radius approach may be used to estimate a friction factor with which to compute friction losses. Under conditions of uniform flow where liquid depth and cross-sectional area do not vary significantly with position in the flow direction, there is a balance between gravitational forces and wall stress, or equivalently between frictional fosses and potential energy change. The mechanical energy balance reduces to tv = g(zx — z2). In terms of the friction factor and hydraulic diameter or hydraulic radius,... 

To evaluate the upstream pressure pi we use the mechanical-energy balance equation (2.7-28) assuming no frictional losses and turbulent flow. (This can be checked by calculating the Reynolds number.) This equation then becomes, for a = 1.0,... 

This is the mechanical-energy loss due to skin friction for the pipe in N m/kg of fluid and is part of the F term for frictional losses in the mechanical-energy-balance equation (2.7-28). This term (Pi—Pz)/ for skin friction loss is different from the (p, — Pz) term, owing to velocity head or potential head changes in Eq. (2.7-28). That part of F which arises from friction within the channel itself by laminar or turbulent flow is discussed in Sections 2.10B and in 2. IOC. The part of friction loss due to fittings (valves, elbows, etc.), bends, and the like, which sometimes constitute a large part of the friction, is discussed in Section 2.10F. Note that if Eq. (2.7-28) is applied to steady flow in a straight, horizontal tube, we obtain (pi — Pz)/p = F. 

The general mechanical energy-balance equation (2.7-27) can be used as a starting point. Assuming turbulent flow, so that a = 1.0 no shaft work, so that Wg = 0 and writing the equation for a differential length dL, Eq. (2.7-27) becomes... 

To derive the equation for the venturi meter, friction is neglected and the pipe is assumed horizontal. Assuming turbulent flow and writing the mechanical-energy-balanCe equation (2.7-28) between points 1 and 2 for an incompressible fluid. 

In practice, the loss term AF is usually not deterrnined by detailed examination of the flow field. Instead, the momentum and mass balances are employed to determine the pressure and velocity changes these are substituted into the mechanical energy equation and AFis deterrnined by difference. Eor the sudden expansion of a turbulent fluid depicted in Eigure 21b, which deflvers no work to the surroundings, appHcation of equations 49, 60, and 68 yields... 

The above interfadal tension results may throw some light on the mechanism of spontaneous emulsification in the present model EC. As mentioned before, there are basically two main mechanisms of spontaneous emulsification, namely creation of local supersaturation (i.e. diffusion and stranding) or by mechanical breakup of the droplets as a result of interfadal turbulence and/or the creation of an ultralow (or transiently negative) interfacial tension. Diffusion and stranding is not the likely mechanism in the present system since no water-soluble co-solvent was added. To check whether the low interfadal tension produced is sufficient to cause spontaneous emulsification, a rough estimate may be made from consideration of the balance between the entropy of dispersion and the interfacial energy, i.e. 

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