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Mud Hydraulics Fundamentals 53

where
v n = nozzle velocity, ft/s or m/s
3
q = mud flow rate, gpm or m /s
2
A T = total nozzle area, in or m 2
The constant 0.32086 becomes 1 in SI units.
Drill bit pressure losses do not result primarily from friction forces but
are due to the acceleration of the drilling fluid through the bit nozzles.
The bit pressure drop is expressed as
ρq 2
Δp b = (2.86)
2
12,031C A 2
d T
where

C d = nozzle discharge coefficient, dimensionless
In the SI system, where Δp b is expressed in kPa, the 12,031 becomes
2,000. The discharge coefficient accounts for the nonideal conditions,
including the viscous frictional effects. Its value has been determined experi-
mentally for bit nozzles by several researchers. They indicated that the
discharge coefficient may be as high as 0.98, depending on the nozzle type
and size, but they recommended a value of 0.95 as a more practical limit.
Since the viscous frictional effects are essentially negligible for flow in short
nozzles, Eq. (2.86) is valid for both Newtonian and non-Newtonian liquids.
An expression of nozzle velocity as a function of pressure drop can be
derived from Eq. (2.86) as

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Δp b
v n = C d −4 (2.87)
8:074 × 10 ρ

The hydraulic power of drilling fluid at the bit is one of the indicators
of the hole-cleaning capacity of the fluid. It is expressed as

P Hb = Δp b q (2.88)
1,714

where

P Hb = bit hydraulic power, hp or w
The constant 1,714 becomes 1 in SI units.