Motors useful equations

It is denoted by C and depends on the flame temperature, mean molecular mass of the combustion products and propellant formulation. It is a fundamental parameter which gives the energy available on combustion and can be used to compare the efficiency of different chemical reactions independently of the Pc. For propellants, the value of C ranges between 1200 and 1600 ms-1. It is determined by firing a propellant grain in a motor and evaluating the area under the P-t profile and using Equation 4.11. 

Both Ta and T vary with speed, and not linearly. Examples of motor and decanter torque/speed curves are shown in Figure 4.15. To use equation (4.137), Ta and T are averaged over the speed range from zero to full motor speed. 

For the fractional-horsepower motor used in the laboratory or pilot plant, power draw is best determined by calculation using the defining equation for the power number. This requires power number versus Reynolds number data or correlation. 

Power, Energy, and Drives. Centrifuges accomplish their function by subjecting fluids and soHds to centrifugal fields produced by rotation. Electric motors are the drive device most frequently used however, hydrauHc motors, internal combustion engines, and steam or air turbines are also used. One power equation appHes to all types of centrifuges and drive devices. 

The brakes should be suitable to counter at least the torque developed by the motor. They must therefore develop at least this amount of torque. To find the least braking torque, the brake drums must be able to develop, in either of the above typies of mechanical brakes, the torque shown in equation (1.10) may be used i.e. 

The following equations are useful in determining the eurrent, voltage, horsepower, torque, and power factors for three phase AC motors ... 

Mathematical models that represent the dynamic behaviour of physical systems are constructed using differential equations. A more accurate representation of the motor vehicle would be... 

Gearbox, lead-screw and machine-table. With reference to Figure 2.9 (free-body diagram of a gearbox), the motor-shaft will have zero viscous friction Cm, hence equation (2.22), using Laplace notation, becomes... 

From Equation 4-138 it is seen that stall torque is proportional to the number of stages used. Thus the stall torque for a turbine motor with 106 stages will be (for the circulation flowrate of 400 gal/min and mud weight of 10 Ib/gal)... 

Total Pressure Loss. Using Table 4-110 and Equations 4-150 and 4-151, the pressure loss across the turbine motor can be determined for the various circulation flowrates and the mud weight of 16.2 Ib/gal. These data together with the above bit pressure loss data are presented in Table 4-113. Also presented in Table 4-113 are the component pressure losses of the system for the various circulation flowrates considered. The total pressure loss tabulated in the lower row represents the surface standpipe pressure when operating at the various circulation flowrates. 

Positive Displacement Motor Performance. Using the positive displacement motor performance data in Table 4-114 and the scaling relationships in Equations 4-168 through 4-170, the performance graph for the positive displacement motor operating with a circulation flowrate of 348 gal/min can be prepared. This is given in Figure 4-213. 

Finally, the thrust F) of a rocket motor is also known to be related to the rate of burning and is obtained via the mass flow rate using the relationship given in equation (3.8) ... 

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