# Hydraulics analysis

## Input(s)

$$N_{1}$$: Jet Size for nozzle 1 (in.)

$$N_{2}$$: Jet Size for nozzle 2 (in.)

$$N_{3}$$: Jet Sizefor nozzle 3 (in.)

Q: Circulation Rate (gpm)

Dh: Diameter of Hole (in.)

Dp: Dia of Drill Pipe (in.)

MW: Mud Weight (psi)

B: Bit Size (in.)

$$P_{s}$$: Surface pressure $$(\mathrm{psi})$$

## Output(s)

AV: Annular Velocity (ft/min)

$$\mathrm{Pb}$$: Bit Nozzle Pressure Loss (psi)

HHP: Hydraulic Horsepower at bit (hp)

HHPba: Power per unit area in sq inc (hp/in. $${ }^{2}$$ )

$$P_{p s i b}$$: Percentage pressure loss at bit (percent)

$$V_{n}$$: Jet Velocity $$(\mathrm{ft} / \mathrm{s})$$

IFa: Impact force per unit area in sq inc (lb/in. $$\left.{ }^{2}\right)$$

## Formula(s)

$\begin{gathered} A V=24.5 * \frac{Q}{D h^{2}-D p^{2}} \\ P b=156.5 * Q^{2} * \frac{M W}{\left(N_{1}^{2}+N_{2}^{2}+N_{3}^{2}\right)^{2}} \\ H H P=P_{s} * \frac{Q}{1714} \\ H H P b a=Q * P b * \frac{1.27}{1714 * B^{2}} \\ P_{p s i b}=P b * \frac{100}{P_{s}} \\ V_{n}=417.2 * \frac{Q}{N_{1}^{2}+N_{2}^{2}+N_{3}^{2}} \\ I F a=M W * V_{n} * Q * \frac{1.27}{1930 * B^{2}} \end{gathered}$

## Reference(s)

Formulas and Calculations for Drilling, Production and Workover, Second Edition, Lapeyrouse, Page: 170.

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