Cv with piping geometric factor consideration equations are:

Where Fp (R)

Where:

d : Valve inlet diameter

D : Internal diameter of the pipe

K : Head loss coefficient of a device,
dimensionless

N2 : constant to suit the measurement
unit, 890

The factor ∑K is the sum of the
effective velocity head coefficient of all fittings.

Where:

K

_{B}: Bernoulli coefficient, dimensionless
K

_{1,2 }: The resistance coefficient for the inlet and outlet fittings, dimensionless**Bernoulli coefficient**is accounted to compensate the changes of pressure due to differences in stream area and velocity.

**Inlet reducer:**

**Outlet increaser :**

**Subscripts**

*1*: Upstream conditions

*2*: Downstream conditions

__Example:__

PV-A case 1:

Cv for Gas sizing is

1 lb/hr x (1 lb-mole/21.5 lb) x
(359.05 std cu ft/ 1 lb-mole) = 16.7 scfh

W = 21088 SCFD = (21088 ft3/day) x (day/ 24 hr) x (1 lb/hr/16.7scfh) = 52.61
lb/hr

X =
72.52/217.56 barg/bra = 0.33

P1 = 15 barg = 217.56 psig

ρ1= 12.15 kg/m3 = 0.7585 lb/ft3

Y = 1 – (x/3*(Cp/Cv / 1.4)*xT)

d
= 1 in (valve size)

D = 2
in (Line size)

Fisher catalog is used as a reference

xT = 0.67 for 80% opening Globe valve

Y = 1 – (0.33 / 3 * (1.263/ 1.4 )
*0.67) = 0.8257

Cv = 52.61 / (63.3 * (0.8257)*(√0.33*217.56*0.7585)

**Cv = 0.1361**(identical value with the Instrucalc 5.1 calculation result)

__Cv with piping geometric factor consideration__

= 1.5 (1 – (1)

^{2}/ (2)^{2 })^{ 2}
= 0.843

Piping Geometric factor

Cv = 17.2 from table.

N

_{2}= 890, from table below
Fp =
(((0.843)*(17.2)

^{2}/ (890)*(1)^{4 }) + 1)^{-1/2}
=
0.883

(When possible it is recommended that
Fp factor be determined by using the specific
valve in actual tests)

Cv = 0.1361 / 0.883

**Cv = 0.1546**

The Cv with Fp factor consideration value is very close to the
Cv used initially for this calculation. (0.1361 versus 0.1546). therefore it
can be neglected.

The
conclusion is that 1 inch valve opened to about 80-percent of total travel
should be adequate for the required specifications.

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