Pipe Reducing Factor

Holden wants to install 1" valve in 2" size pipe. But he wonder what are the reducing factor that he needs to consider. So he began to make the calculation.


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.

               N₂ = 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.