Flow rate Froude numbers

In the set of conservation equations described earlier, the Reynolds number and the Froude number must be the same for the model and the prototype. Since most industrial operations involve turbulent flow for which the Reynolds number dependence is insignificant, part of the dynamic similarity criteria can be achieved simply by ensuring that the flow in the model is also turbulent. For processes involving hot gases (i.e., buoyancy driving forces), the Froude number similarit) yields the required prototype exhaust rate as follows. 

On the other hand, since the film is accelerating in this initial zone, it follows that the Froude number of the flow, which may be taken as the criterion for gravity-wave instability, increases from some very small value at the inlet to its equilibrium value for the particular flow rate and channel slope. Depending on the flow conditions, it is possible for the Froude number of the flow to reach the critical value before the end of the acceleration zone is reached. In this case it can be supposed that waves could occur before the end of the acceleration zone if some triggering mechanism were available. This appears to be the case in fact, for Tailby and Portalski (T5) have noted that when an adjacent gas stream (either cocurrent or countercurrent) is present, the length of the smooth entry zone decreases markedly. 

The flow rate required for the transition from regimes a to b or b to c is correlated to the Froude number and other system parameters, as shown in Table VI. The flowrate for the a-b transition depends on the direction in which JV is changed, as well as on the reactor scale (Zlokarnik and Judat, 1967). Van t Riet and Smith (1975) showed that the dispersion does not occur if Fr < 0.1. The aeration number for the b-c transition is mainly a function of the Froude number. 

For a given fixed flow rate Q = Vbh, and channel width profile b(x), Eq. (6-56) may be integrated to determine the liquid depth profile h x). The dimensionless Froude number is Fr = Vbgh. When Fr = 1, the flow is critical, when Fr < 1, the flow is subcritical, and when Fr > 1, the flow is supercritical. Surface disturbances move at a wave velocity c = they cannot propagate upstream in supercritical... 

Calculate the Froude numbers and flow conditions for the 2-, 4- and 6-inch (Schedule 40) vertical pipes having the following liquid and vapor flow rates and densities. 

For each experiment, the upstream flow rate was recorded to compute the upstream flow speed and the corresponding Froude number. Then the gauge was placed at the location of the jump end of each Froude number according to the Bradley-Peterka curve [32], The upstream water depth yi was recorded and then the downstream water depth y2 can be estimated by Equation (3.88). 

Froude number, UG/d g gravitation constant volumetric gas flow rate Henry coefficient... 

D Mean particle size, mm F Bed frequency of oscillation, s Solids mass flow rate, kg/s Fr Froude number for slurry flow in the drum, V/[2 g R (Ss - 1) ] Fr, Modified Froude number for pipe... 

F factor through active area F factor through hole area F factor through total tower cross-sectional area molar flow rate of feed to stage , kmol/s packing factor, m Froude number, dimensionless gravitational constant, 9.81 m/s ... 

The effect of temperature on the corrosion rate for brine under various conditions of carbon dioxide partial pressure and Froude number is shown in Fig. 6-20. It is seen that at a given carbon dioxide partial pressure and Froude number, the corrosion rate increases with increasing temperature over the entire range of temperatures studied, and no maximum in the corrosion rate is observed at any temperature studied. These increased rates of corrosion at higher temperatures (above 70 °C) and pressures are not predicted by the existing, well-known results for full pipe flow under similar conditions, which have been used in design calculations. The results for corrosion... 

The Froude number allows the effect of slug flow turbulence on the corrosion rate to be correctly quantified. Specifically, the pressure drop across the slug is used as a measure of the effect of the turbulence and, as mentioned, this can be related to the enhanced mass transfer. From Fig. 6-21, it can be seen that the corrosion rate varies exponentially with respect to pressure drop across the slug. The value of the exponent is constant at around 0.3. This is an important result which comes from using the Froude number in the film as defined by Eq. (6-1). 

In the above relations, Re is the Reynolds number, mo is the liquid flow velocity at the nozzle outlet, d i is the inner diameter of the nozzle, vl is the kinematic viscosity of liquid, Fr is the Froude number, g is the acceleration due to gravity, is the density of liquid. We is the Weber number, a is the surface tension of liquid, is the velocity ratio defined subsequently, and 2g is the gas flow rate. 

Figures 11.9 and 11.10 present the dependence of the relative length Ljd (L -flame length, d - nozzle diameter) of the turbulent flame on the Froude number Fr = U / gd), U - flow rate at the nozzle exit section, g - free fall acceleration. It is seen that in the low-Froude number region (less than 10 ), the experimental data are well described by the interpolated relation [24]...

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