Blade to gas speed ratio

Considering now Figure 15.4(b), when the blade to gas speed ratio is higher than the design value, the angle... 

Thus the blade-to-gas speed ratio at which the blade will abstract no useful work is Rb = 1.41 when ai = 20°. This is indicated in Figure 15.6 by the blade efficiency falling to zero at this point. 

Hence, making use of the moving blade to gas speed ratio, Rb, we may write ... 

Equation (A7.28) is an implicit equation in the three variables blade to gas speed ratio, Rg, degree of reaction, p, and temperature ratio, r. The temperature ratio, r, itself may be regarded as a function of degree of reaction, p, and stage pressure ratio (pa/Po) since, from (A7.23) and (A7.24),... 

We may therefore find consistent values of (p2/po)< P and Rg, by specifying both the pressure ratio, (P2/P0). and the blade to gas speed ratio, Rg, and then adjust the reaction ratio, p, iteratively so that equations (A7.30) and (A7.28) are each satisfied. 

Consider first the situation in Figure 15.4(a), when the blade speed to gas speed ratio is lower than the design value. The incoming gas will strike the back face of the blade at the inlet. The main stream of gas will then flow immediately along the blade-tip face into the main... 

As a result, the blade speed to gas speed ratio will depend solely on the gas speed leaving the fixed blades ... 

It is important to emphasize the limitations on the use of this equation. It is essentially a design equation and it represents the variation in blade efficiency with blade/gas speed ratio for a turbine impulse blade under the following conditions ... 

The performance of an operational turbine stage will be governed by the total stage pressure ratio, (P7/P0), and to the blade speed to nozzle-outlet gas speed ratio. Changes in the conditions away from the design point will be characterized by alterations to either or both these parameters. We will now consider how the degree of reaction is affected by such changes. 

Defining Rg as the ratio of blade average linear speed to mid-stage gas speed,... 

Since we know the gas speed at the exit of the nozzle, we may calculate the ratio of gas speed to nozzle outlet speed, Rp. If the stage is an impulse stage we calculate the blade efflciency at off-design conditions using equations (15.50) and (15.66). The specific work of the stage will then be given by ... 

Characteristic length [Eq. (121)] L Impeller diameter also characteristic distance from the interface where the concentration remains constant at cL Li Impeller blade length N Impeller rotational speed also number of bubbles [Eq, (246)]. N Ratio of absorption rate in presence of chemical reaction to rate of physical absorption when tank contains no dissolved gas Na Instantaneous mass-transfer rate per unit bubble-surface area Na Local rate of mass-transfer per unit bubble-surface area Na..Average mass-transfer rate per unit bubble-surface area Nb Number of bubbles in the vessel at any instant at constant operating conditions N Number of bubbles per unit volume of dispersion [Eq. (24)] Nb Defined in Eq. (134)... 

A mechanical pump providing even lower vacuum levels is the turbomolecular pump, in which one or more balanced rotors (turbine blades) spin at 20,000 to 50,000 rpm. At these rotation rates, the periphery moves at a speed that exceeds the mean molecular speeds of most molecules, and gas-rotor collisions impart a momentum component to the gas in the direction of the exhaust. Compression ratios up to 10 can be achieved as long as the outlet pressure is kept below about 0.1 Torr by a forepump. 

The multiplying constant for concave-blade disk turbines is 0.058 instead of 0.025. This constant has a weak dependence (to the power of about 0.2) on the scale of the equipment. This inequality defines two regions delimited by a vertical line in the Fr vs. Flo flow map, for a given value of the D/T ratio. Nienow, Wisdom, and Middleton developed a relationship to predict the agitation speed of a flat-blade disk turbine at which gas recirculation occurs for a given gas rate. This expression... 

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