Froude number liquid

For NRc S 10, the liquid motion moves with the impeller, and off from the impeller, the fluid is stagnant [34]. The Froude number accounts for the force of gravity when it has a part in determining the motion of the fluid. The Froude numbers must be equal in scale-up situations for the new design to have similar flow when gravity controls the motion [16]. 

Similarly it may be shown that, at the critical conditions, the flowrate is a maximum for a given value of the specific energy J. At the critical velocity, (ir/gD) is equal to unity. This dimensionless group is known as the Froude number Fr. For velocities greater than the critical velocity Fr is greater than unity, and vice versa. It may be shown that the velocity with which a small disturbance is transmitted through a liquid in an open channel is equal to the critical velocity, and hence the Froude number is the criterion by which the type of flow, tranquil or rapid, is determined. Tranquil flow occurs when Fr is less than unity and rapid flow when Fr is greater than unity. 

Froude number based on superficial liquids velocity Froude number based on superficial gas velocity Nusselt number based on liquid parameters... 

The effect of various parameters on the difference between vapor and liquid pressure is illustrated in Figs. 8.3 and 8.4. The effect of the Fuler and Weber numbers as well as the thermal parameter is highly noticeable. An increase in Fu, We and d- leads to a decrease in AP, whereas the difference of both phase pressures is practically independent of Reynolds number. An increase in the Froude number is accompanied by an increase in AP for a small Fr. At Fr > 10 the effect of Fr on AP is negligible. 

The difference in pressure between vapor and liquid within the evaporation region depends mainly on the Euler and Weber numbers, as well as on the thermal parameter The effect of the Reynolds and Froude numbers on the pressure difference of both phases is negligible. 

The correlation of Norwood and Metzner shows to be a complex function of the Reynolds number, the Froude number, the ratio of tank-to-impeller diameter, and the ratio of tank diameter to liquid level. However, to a reasonable first approximation for geometrically similar vessels operating at high Reynolds numbers. 

The Froude number (Fr) is the ratio of the inertial force to the gravitational force of the liquid ... 

In liquid mixing systems, baffles are used to suppress vortexing. Since vortexing is a gravitational effect, the Froude number is not required to describe baffled liquid mixing systems. In this case the exponent y in equations 5.17 and 5.18 is zero and FryM = 1. 

For scale-up from system 1 to system 2 for the same liquid properties and system geometry, equation 5.14 which defines the Reynolds number for mixing ReM, equation 5.15 which defines the Froude number for mixing FrM, and equation 5.16 which defines the Weber number for mixing WeM, can be written respectively in the following forms ... 

At values of a Froude group of less than unity, particulate fluidisation normally occurs and, at higher values, aggregative fluidisation takes place. Much lower values of the Froude number are encountered with liquids because the minimum velocity required to produce fluidisation is less. A theoretical justification for using the Froude group as a means of distinguishing between particulate and aggregative fluidisation has been provided by Jackson and Murray . 

Hughmark (Hll) has extended this approach to obtain an empirical correlation covering wide ranges of data for the air-water systems in vertical flow. Basically the correlation consists of using Eq. (70) with a variable value of the coefficient K. This coefficient was expressed by Hughmark as a function of the mixture Reynolds number, Froude number, and liquid volume-fraction. Hughmark s approach gives... 

Dl. Davis, W. J., Effect of the Froude Number in Estimating Vertical Two-Phase Gas-Liquid Friction Losses. Presented at A.I.Ch.E. Nat. Meeting, Los Angeles, February, 1962. 

In liquid systems, we can suppress the effect of the Froude number by using baffles to eliminate vortexing and hence the gravitational effects. The Weber number is of some importance only when separate physical phases are present in the liquid mixing system. 

This definition of 2VFr is of particular physical significance in film flow, since here the Froude number denotes the ratio of the mean film velocity to the celerity of a gravity wave in shallow liquid. (Wave celerity is defined as the velocity of a wave relative to the liquid on which the wave propagates.) The Weber number is defined by analogy. 

Stichlmair and Fair (Distillation Principles and Practice, Wiley -VCH, New York, 1998) show that liquid holdup is primarily a function of the liquid Froude number, specific surface area of the packing, and physical properties. They recommend the correction by Engel, Stichlmair, and Geipel [Ind. Eng. Chem. Symp. Ser. 142, 939 (1997)]. 

The Froude number is associated with the formation of a vortex on the liquid free surface around the impeller shaft. At low impeller speeds... 

It is decided to model a full-scale prototype, unbaffled, stirred vessel with a one-tenth scale model. The liquid in the prototype has a kinematic viscosity, v. of 10 7 m2 s As we have seen above, power number is a function of both Reynolds number and Froude number for unbaffled vessels. To ensure power number similarity, we need to ensure both Reynolds number and Froude number are similar from prototype to model. 

Froude number of the liquid. Given by Eq. (8.20) for the Bravo et al. pressure drop correlation, and by Eq. (9.18) for the Bravo and Fair efficiency correlation, dimensionless... 

Q-1 represents the reciprocal value of the well known gas throughput number Q. Fr is the Froude number, here formed with the gas throughput and cT is the dimensionless concentration (in ppm) of the foaming agent in the liquid. S are the physical properties which affect foam stability. Because they are neither known by number (i) nor by kind, instead of S the type of the foaming agent (name and chemical structure) must be given. 

In dealing with this question, we should first look at the flow conditions at the liquid surface. It is well known that longer waves move faster than shorter ones and that large ships can travel faster than small ones. Both things have to do with the wave formation at the liquid surface, for which the gravitational acceleration, g, is also characteristic of. Therefore, the motion of a body at the liquid surface is dependent on the Froude number, Fr. From the structure of this pi-number... 

The surface tension a and the dynamic viscosity of the liquid /i (as long as it is low) do affect gas flowrate. For viscosities greater than 0.5 PaS, however, the use of hollow stirrers for aeration becomes meaningless. Since aeration deals with a material system with large density differences, the operation is strongly influenced by the parameter gAp/p g at normal pressure, and therefore by the Froude number. 

The gas throughput characteristic of a hollow stirrer generally has the form /VA = /(Fr dy H, Ga, dr/dt, HJdf), where NA = qt/(Ndf) is the dimensionless flowrate number, Fr s Ndjg the Froude number, and Ga = dfg/v2 the Galileo number. For liquids with viscosities close to that of water and for HJd = 1, the gas throughput characteristics for the tube stirrer shown in Fig. 9 are as follows ... 

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