Geometry similarity

The speeifie speed eompares the head and flow rate in geometrieally similar maehines at various speeds... 

Equality of all groups in Equation 7-13 assures similarity between systems of different sizes. The types of similarity are geometrie, kinematie, and dynamie. The last tliree terms of Equation 7-13 represent the eonditions for geometric similarity, whieh require that all eor-responding dimensions in systems of different sizes have the same ratio to eaeh other. Eor geometrie similarity, Equation 7-13 beeomes... 

Kinematic similarity exists between two systems of different sizes when they are geometrieally similar and when the ratios of veloeities between eoiresponding points in one system are equal to tliose in tlie otlier. 

For seale-up from system 1 to system 2 involving geometrieally similar tanks and same liquid properties, the following equations ean be applied ... 

Seraper blades set to rotate at 35 rpm are used for a pilot plant addition of liquid ingredients into a body-wash produet. What should the speed of the blades be in a full-seale plant, if the pilot and the full-seale plants are geometrieally similar in design Assume seale-up is based on eonstant tip speed, diameter of the pilot plant seraper blades is 0.6 m, and diameter of the full-seale plant seraper blades is 8 ft. 

During liquid makeup produetion, eolor pigments (i.e., solid having identieal partiele size) are added to the produet via a mixer. In the pilot plant, this mixer runs at 6,700 rpm and has a diameter head of 0.035 m. Full-seale produetion is geometrieally similar and has a mixer head diameter of 0.12 m. Determine the speed of the full-seale produetion mixer head. What additional information is required for the motor to drive this mixer Assume that power eurves are available for this mixer design, and the seale-up basis is eonstant power/unit volume. 

The draft tubes of the reaetor are hollow in order to allow eooling or heating fluid to eireulate. The 300-ml laboratory-seale reaetor (1) is geometrieally similar to the larger reaetors. A marine-type impeller (propeller) provides a smooth and even flow field throughout the reaetor. 

Correction factor for scale-up using non-geometry similarity,... 

A dimer made up of two zinc porphyrins bearing a 7-azabicy-clo[2.2.1]heptadiene fused at the C2-C3 /3-positions was reported by Knapp (61). The compound was designed to dimerize with a pyrrole-over-pyrrole geometry similar to that found in the photosynthetic special pair. Dimerization at KT3 M was confirmed by VPO and JH NMR spectroscopy. Dilution to 10-5 m or addition of DMAP caused disaggregation of the complex. In the solid state, this compound assembles as a cyclic hexamer with the vicinal porphyrin planes almost perpendicular. 

In a metalloid cluster [2] more metal-metal bonds than metal-ligand bonds are involved, which means n > r. The largest structurally characterized compounds of this type contain 77 A1 or 84 Ga atoms, respectively [3, 4], Metal-metal bonds dominate these clusters and the framework of the resulting metal-metal bonds exhibits a geometry similar to the bulk metal itself. With respect to the Greek word ei8o< (idea, prototype) the suffix -oid indicates that the bulk metal element is actually visible in the metal atom core of the metalloid or more generally, elementoid clusters. 

As can be seen in Figure 39, the nitride monoanion [Fe4(CO)12N] has a butterfly geometry similar to that of [Fe4(CO)i2C]2-, even if the wings are considerably less open.ld... 

SOFCs can have a planar geometry similar to PEFCs, but the leading technology is tubular, as shown in Fig. 24-54. The advantage of the tubular arrangement is the absence of high-temperature seals. 

As Stated above, both Ws(z) and are fixed by the geometry of the screw. A schematic representation of the solid hed in the channel is shown in Fig. 6.25 for a barrier section geometry similar to that of Fig. 6.23(a). This representation depicts how the four films change In dimension as the solid bed is consumed in the melting section of the screw. 

In an early attempt to model the dynamics of the chromatin fiber, Ehrlich and Langowski [96] assumed a chain geometry similar to the one used later by Katritch et al. [89] nucleosomes were approximated as spherical beads and the linker DNA as a segmented flexible polymer with Debye-Huckel electrostatics. The interaction between nucleosomes was a steep repulsive Lennard-Jones type potential attractive interactions were not included. 

The lanthanides in several complexes exhibit mixed (promiscuous) coordination numbers and geometries, similar to the presence of mixed oxidation states in a inorganic compound. We shall only discuss a few cases here to make the readers aware of this interesting situation. 

---