Froude’s number

Frequency of particles of stated size Froude s number Fanning s factor... 

The Froude s number characterizes the influence of gravity on liquid s motion. In many problems Fr 1, that is, the gravity exerts weak influence on the flow, therefore the last term in the right part (5.107) can be neglected. 

In this model several correlations are used. In order to determine which of them applies, Froude s number is needed. It is given by... 

Froude number. Considering inertia and gravity forces alone, a ratio is obtained called the Froude number or Froude s law, in honor of William Froude, who experimented with flat plates towed lengthwise through water in order to estimate the resistance of ships due to wavemaking. The force of gravity on any body with a linear dimension L is... 

To achieve a dynamically similar flow condition in a scaled model, the Froude number F, the Reynolds number R, and the Euler number E should match those of the prototype. When the flow is transient, the Strouhal S number should be matched as well. These parameters are defined as ... 

The centrifugal force will draw the gas into the system, which ensures that sufficient turbulence is created. For this, a power input greater than 100 W/m3 is required from the agitator.6 Alternatively, a tip speed (irND) greater than 1.5 m/s or a Froude number (A D/g) greater than 0.1 are often used, where N is the agitator speed in Hz, and g is gravitational acceleration in m/s2. 

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]. 

Pattern transition in horizontal adiabatic flow. An accurate analysis of pattern transitions on the basis of prevailing force(s) with flows in horizontal channels was performed and reported by Taitel and Dukler (1976b). In addition to the Froude and Weber numbers, other dimensionless groups used are... 

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... 

Moog and Jirka then calibrated the lead coefficient and studied the predictive capability of 10 calibrated empirical equations to predict reaeration coefficients that were the result of 331 field studies. The result was surprising, because the best predictive equation was developed by Thackston and Krenkel s (1969) from laboratory flume studies, and the comparison was with field equations. In dimensionless form, Thackston and Krenkel s (1969) cahbrated (multiplying the lead coefficient by 0.69) equation can be converted to a dimensionless form utilizing Sherwood, Schmidt, Reynolds, and Froude numbers ... 

Gliksman s approach The result of the conversion of equations into nondimensional ones is a set of dimensionless parameters (Froude number, velocity, particle size, diameter ratios, etc.) that should be matched in both small and large systems. It is not necessary for the values of the parameters to be equal in each system. Instead, the dimensionless number ratios have to remain the same. To achieve this, the particle size and/or the particle density of the solids have to be changed appropriately in the small unit. It usually results in a smaller particle size in the small unit compared to the large one. 

It is noted here that the Froude number has changed and that dynamic similarity cannot be maintained if both, the model fluid viscosity and the model tank dimensions, are fixed because two unknowns (D and Q) are required to satisfy the two eqns. (4.64) and (4.65). Since gravity is a constant (9.81 m/s2) and p//t= 1,000 s/m2 is fixed for the model, obtaining that... 

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. 

In previous paragraphs, we obtained groups of dimensionless vaiiables by means of Buckingham s theorem. In the development of Reynolds, Froude, and Weber numbers we utilized the concept of force ratios although the same numbers can be produced by means of Buckingham s theorem. 

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. 

Two additional experiments were carried out, not with the model ship, but with a totally immersed form (Fig. 5) whose shape was given by reflecting the immersed portion of a ship s hull at the water line (at V/l3 = idem). In these experiments, the Froude number is irrelevant the friction corresponding to the surface area of the model must be divided by 2. 

Due to water displacement, a ship produces waves at travelling. A bow wave, a few waves along the ship s hull and a stern wave are created. At full speed, the so-called hull speed , it is left with a bow wave and a stern wave, the two separated by the length of the ship s hull. The critical value of the Froude number at this state is Fr = 0.16. Going faster than this requires that the ship leave its beneficial stern wave astern and try to cut through or climb up its bow wave. Both would result in a dramatic rise in power demand. 

The critical value of the Froude number shows why decent surface speeds are off-limits for the sizes of most of Nature s vessels and why even air breathers mostly swim submerged. An occasional animal porpoises up and down through the interface or planes on the surface, but only a large whale could consider migrating as a surface ship. 

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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