STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

868 Drilling and Well Completions
The stall torque Ms (ft-lb) for any turbine motor can be determined from [86]
where q, = hydraulic efficiency
q, = mechanical efficiency
n, = number of stages
7, = specific weight of mud in lb/gal
q = circulation flowrate in gal/min
p = exit blade angle in degrees
h = radial width of the blades in in.
(4-138)
Figure 4-193 is the side view of a single-turbine stage and describes the geometry
of the rotor and stator.
The runaway speed Nr (rpm) for any turbine motor can be determined from
(4-139)
where qv = volumetric efficiency
rm = mean blade radius in in.
The turbine motor instantaneous torque M (ft-lb) for any speed N (rpm) is
M = Ms(l-$)
(4-140)
The turbine motor horsepower HP (hp) for any speed is
2 nM ,N
HP = -
33,000 (’- $)
(4-141)
The maximum turbine motor horsepower is at the optimum speed, No, which
is one-half of the runaway speed. This is
N
No = I (4-142)
2
Thus the maximum horsepower HP,,, is
HP,,
= xMJ,
2( 33,000)
(4- 143)
The torque at the optimum speed M, is one-half the stall torque. Thus
M, M, = - 2
(4-144)