Critical bed depth

The critical bed depth (Z0) was found to be 0.8 cm. When the column capacity at breakthrough was compared with batch capacity at the same concentration, the... 

Critical Bed Depth In a carbon column the critical bed depth is the depth of granular carbon that is partially spent. It lies between the fresh virgin carbon and the spent carbon, and is the zone where adsorption takes place. In a single-column system this is the amount of carbon that is not completely utilized. 

Na is the adsorption capacity, is the adsorption rate parameter and F is the flow rate. The critical bed depth, Zq, is the theoretical depth of carbon sufficient to prevent the solute concentration from exceeding the Q value at f = 0. By letting / = 0, Zo is obtained by solving Eq. (15.31) for Z. The final result is ... 

The critical bed depth is the theoretical depth of adsorbent that is just sufficient to prevent the effluent concentration from exceeding Cb at zero time and clearly is equal to the mass transfer zone length MTZL described above. The critical bed depth may be calculated by substituting r = 0 into equation (6.55) ... 

To convert feet per second to meters per second, multiply by 0.305 to convert pounds per cubic foot to kilograms per cubic meter, multiply by 16. In SI units, g = 9.8 m/s. The inlet orifice diameter, air rate, bed diameter, and bed depth were all found to be critical and interdependent ... 

Packed bed heights typically vary from 20 ft to 30ft. Many times the location of manholes to provide access to the redistributor will determine the packed depth. Whenever more than 15 theoretical stages are required in one packed bed, good liquid distribution is critical. ... 

The M1 scenario. This is a mild slope case. The most common case of backwater is where the depth is already above the critical and is increased still further by a dam. Referring to the specific energy equation, Eq. (10.116), as the depth increases, the velocity diminishes without any abrupt transitions, so that a smooth water surface plane is obtained. In the case of flow in an artificial channel with a constant bed slope, the backwater curve would be asymptotic at infinity to the surface for uniform flow, as noted before. But the problems that are usually of more important interest are those concerned with the effect of a dam on a natural stream and the extent to which it raises the water surface at various points upstream. 

The M3 scenario. This occurs because of an upstream control, as by the sluice gate. The bed slope is not sufficient to sustain lower-stage flow, and, at a certain point determined by energy and momentum relations, the water surface will pass through a hydraulic jump to upper-stage flow unless this is made unnecessary by the existence of a free overfall before the M3 crest reaches critical depth. 

In the velocity theory above developed it is apparent that while fundamentally sound, the chief difficulty in practice concerns the measurement of bed velocities. This has been overcome in part by Rubey s analysis of the subject, and By the general theory of Kennedy and Lacey. However, in recent years studies of silt movement have utilized DuBoys (1879) expression of tractive force. This expression is simple and convenient and involves the basic elements of channel hydrology depth and slope. Tractive force means the force activity on the bed causing movement of the particulate material. The force required to impart initial motion to the bed material is called the critical tractive force. General movement is defined as the condition where particles up to and including the largest composing the bed are in motion. 

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