## IV. PUMP APPLICATIONS

### E. Sizing a WGI Pump for High Inlet Pressure Conditions

**1. **For double acting piston pumps, no derating is
required.

**2.** For a single acting plunger pump, where the *rod
load* due to inlet pressure is less than 20% of full plunger/rod load, no derating
required.

**3.** For a single acting plunger pump (with __standard__
bronze wrist pin bushings), where the *rod load* due to inlet pressure is greater
than 20% of full plunger/rod load, derating is as follows:

**a. **For triplex pumps, add two-thirds the inlet/suction
pressure to the discharge pressure in selecting the pump maximum plunger pressure.

**b.** For quintuplex pump, add two-thirds the
inlet/suction pressure to the discharge pressure in selecting the pump maximum plunger
pressure.

**4.** For a single acting plunger pump (with __optional__
wrist pin roller/needle bearings), where the *rod load* due to inlet pressure is
greater than 20% of full plunger/rod load, no derating is required* *if __both__
of the following requirements are met;

**a.)** *inlet/suction pressure is less than 50% of the
maximum plunger pressure rating*

**b.) ***discharge pressure is less than the maximum
plunger pressure rating.*

V. SUPPLY SYSTEM CONSIDERATIONS

**A. Pressure**

Liquid pressure is defined as the normal component of force per unit
area. In common practice and general function, pressures are frequently measured in pounds
force per square inch (lbf/in^{2}). Gauge pressure (psig) is the difference
between absolute pressure (psia) and the atmospheric pressure (P_{a}). Appendix A,
Table 7 shows the relationship between atmospheric pressure and elevation. Vapor pressure
is the absolute pressure exerted by the liquid and its vapor to maintain an equilibrium
condition at a given temperature of the liquid.

**Example 7:**

Find vapor pressures of water at 76°F and 212°F at sea level..

From Appendix E - *Table of Vapor Pressure of Water*:

The vapor pressure of 76°F water is 0.4443 psia at sea level.

The vapor pressure of 212°F water is 14.696 psia at sea level.

**B.** Head

The English unit for measuring head is feet. The equation, expressing pressure (psi) in units of feet, is:

Head = __psi x 2.31 __

S.G.

Where,

S.G. = Specific Gravity @ pumping temperature.

**Example 8:**

Find the head in units of feet (ft.) of crude oil, with a S.G. = 0.8 @ pumping temperature, at 20 psi pressure.

Head = __20 x 2.31__ = 57.75 ft.

0.8

**Example 9:**

Find the head in units of feet (ft.) of mercury with a S.G. = 13.6 @ pumping temperature), at 20 psi pressure.

Head = __20 x 2.31__ = 3.39 ft.

13.6

**C. **Viscosity

Basic metric viscosity units are the *poise* (absolute/dynamic viscosity) and the *stokes*
(kinematic viscosity). More customary expression of these units are *centipoise* and *centistokes*
respectively, each equal to 1/100th the of basic metric viscosity unit. The relationship
between the English units for medium viscosity liquids, SSU (Saybolt Universal Seconds),
and metric absolute viscosity is:

n (absolute viscosity, *centistokes*) = 0.22 (SSU) - __180
__

(SSU)

Introducing the mass density of the liquid (r) allows the expression of the relationship between absolute viscosity to Kinematic viscosity as follows:

m (Kinematic viscosity,* centipoise*) = rn

**Example 10:**

Find viscosity in *centistokes* (n) and *centipoise*
(m) of a liquid with S.G. = 0.8 with a viscosity of 500 SSU.

n = 0.22 (500) - __180__ = 109.64 *centistokes*

500

Then,

m = 0.8 x 109.64 = 87.71 *centipoise*

The basic pump speed, and its relationship with various ranges of liquid viscosity, are discussed in further detail in Appendix A.

**D. **Frictional head losses

Pipe, valves, fittings, hoses, and meters installed in the liquid supply piping system generate resistance to the liquid flow. The friction head is the hydraulic pressure required to overcome frictional resistance of a piping system. The Table in Appendix C shows an equivalent length in feet, of 100 percent opening valves and fittings. Pressure drop in liquid lines versus liquid flow rates is shown in Appendix D.

E. Reynolds Number

The Reynolds Number* *(R_{e}) is
used in closed conduit/pipe flow, deals with the viscous force in a liquid, and is defined
by the following equation:

R_{e} = __r___{1}__
d___{f}__ n___{1}

m_{1}

_{}

Where,

R_{e} = Reynolds Number

r_{1} = liquid density at flowing temperature,
lbm/ft^{3}

^{}

d_{f} = pipe inside diameter, feet

n_{1} = liquid flow velocity, ft/sec

m_{1} = liquid viscosity

(*centipoise* divided by 1488 or *centistokes* multiplied by S.G. then
divided by divided by 1488)

Customarily;* turbulent* *flow* occurs when the R_{e} is greater than 3000,* laminar flow* occurs when the R_{e} is less than 2000. The *transition period* is when the R_{e} is between 2000 and 3000.

**Example 11:**

A 14" schedule 30 piping system is designed to deliver 18,970 BPD
(553.3 GPM) of crude oil with a Kinematic viscosity of 50 *centistokes* and S.G. =
0.8 @ 100°F.

Find the Reynolds Number (R_{e}).

**R _{e} = r_{1}
d_{f} n_{1}
= 49.92 x 1.104 x 1.28**

m_{1} 0.02688

R_{e} = 2624.2

Where,

r_{1} = 62.4 x 0.8 = 49.92 lbm/ft^{3}

d_{f} = 13.25 = 1.104 feet

12

n_{1} = 553.3 = 1.28 ft/sec

2.45 (13.25)^{2}

m_{1} = 50 x 0.8 = 0.02688

1488