STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

The bit hydraulic horsepower HP, is
Drilling Bits and Downhole Tools 787
HP, = - q*P,
1714
(4-77)
Jet nozzle impact force F,(lb) is
F, = 0.01823 Cq(yAP,)'/' (4-78)
The velocity of flow from the nozzles v,(ft/s) is given by
(4-79)
where q,, q,, q, = the volumetric flow rate from each nozzle in, ft3 s
A,, A,, A, = the cross-sectional area of each nozzle (Le., Ai = (71/4)di2) in ft2
The total volumetric flow rate q (ft'/s) can also be expressed as
q = V,(A, +A, +A,) = VnA,
(4-80)
where
A, = A; + A, + A,
The nozzle velocity vn(ft/s) is
- Q
v,, = -
3.117a,
(4-81)
where at = the total nozzle area, in.2
The maximum cross flow velocity under the bit, vc(ft/s), is [48]
(4-82)
where dn = the borehole diameter in in.
n = the number of open nozzles
Figure 4-143 gives convenient graphs for nozzle selection for roller rock bits [47].
Example
Determine the pressure drop across the bit and the velocity of the nozzle flow
where the total rate of flow through the drill string (and bit) is 300 gal/min,
the specific weight of the mud is 12.0 Ib/gal, and the three nozzle openings
are to be in. in diameter. Use c = 0.95.
The pressure drop across the bit is found by equation 4-76.