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PRINCIPLES OF FLUID FLOW

There are two types of fluid flow in pipelines:

1. Single-phase flow : either gas or liquid

2. Two-phase flow (multiphase-flow): a

mixture of gas and liquid

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Streamline flow (laminar or viscous).

Turbulent flow

Stages of Flow

- Low Velocity : Streamline or laminar flow

- Medium Velocity : Unpredictable flow (both

streamline and turbulent)

- High velocity : Turbulent Flow

Reynolds Number (NR)

A dimensionless number used to determine the type of flow

NR = 7740 dv

SINGLE-PHASE FLOW

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Reynolds Number (NR) (Contd)

d = Pipe inside diameter, in

V = Velocity of flow, ft/sec.

= fluid kinematic viscosity, centistokes.

NR < 2000 Streamline flow

2000 < NR < 4000 Unpredictable flowNR > 4000 Turbulent flow

SINGLE-PHASE FLOW

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Using Pipeline Units

NR = 419.128 x Q x SSU

d(SSU2 - 818.56)

Q = flowrate, BPD

SSU = Viscosity in SSUd = inside diameter of pipe, in

Prediction of Pressure Losses in Pipelines

Two formulas are used for this purpose:

a. Hazen & Williams Formula

f = 0.2083 100 1.85 x q1.85

C d4.8655

SINGLE-PHASE FLOW

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Prediction of Pressure Losses in Pipelines (Contd)

f = friction head, ft/100ft of pipe

c = constant accounting for pipe roughness

q = flowrate, GPM

d = inside diameter of pipe, in

b. Darcy or Fanning Equation

hf = f L . V2

D 2g

hf = frictional resistance, ft.

L = Length of line, ft

D = inside diameter of pipe, ft

g = gravitational constant, 32.2 ft/sec2.

f = friction factor, dimensionless.

SINGLE-PHASE FLOW

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b. Darcy or Fanning Equation (Contd)

When expressed in oil industry units:

hm = 0.13985 fQ2 or Pm = 8.567 fQ

2 .

D5 D5(131.5 + API)

hm = head loss, ft/mile

f = friction factor, dimensionless

Q = flowrate, BPD

D = inside diameter of line, in

Pm = pressure loss, psi/mile

Prediction of Pressure Losses in Gas Pipelines

P100 = W2 (0.000336f) ( d5 )

SINGLE-PHASE FLOW

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Prediction of Pressure Losses in Gas Pipelines (Contd)

P100 = pressure loss, psi/100ftW = mass flowrate, lb/hr

d = inside diameter of pipe, in

f = friction factor, dimensionless

= density, lb/ft3 = MW x P (psia) .10.73 x T (R) x Z

Setting C1 = W2 x 10-9 and C2 = 336000f

d5

P100 = C1 C2Graphs and charts are available for determination of C1 and C2

SINGLE-PHASE FLOW

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Two-Phase Flow

Calculations of pressure loss are complex and need much computer

work. This is beyond the scope of this course.

Factors Affecting Pressure Losses in Pipelines

- Density and viscosity of the fluid

- Flowrate or fluid velocity

- Pipeline Size

- Pipeline Length

- Pipe Roughness- Flow Restrictions : Valves, Chokes etc.

- Pipe Fittings

- Changes in Elevation

SINGLE-PHASE FLOW

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Head Loss in Valves and Fittings

Convert pressure drop to equivalent length of piping (same diameter of

pipeline).

Bernoullis Theorem

P1 . + V12 . + Z1 = P2 . + V2

2 . + Z2 + hf1 2g 2 2gWhere hf is the head loss due to friction and control devices between

points 1 & 2

SINGLE-PHASE FLOW

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PRINCIPLES OF FLUID FLOW

MODULE - 2