Gas Side Pressure Drop Across Tubes
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The gas side pressure drop may be calculated by any number of methods available today, but the following procedures should give sufficient results for heater design.
Bare Tube Pressure Loss:
For bare tubes we can use the method presented by Winpress(Hydrocarbon Processing, 1963),
Dp = Pv /2 * Nr
Where,
Dp = Pressure drop, inH2O |
Pv = Velocity head of gas, inH2O |
Nr = Number of tube rows |
And the velocity head can be described as,
Pv = 0.0002307 * (Gn /1000)2 / rg
Where,
Gn = Mass velocity of gas, lb/hr-ft2 |
rg = Density of gas, lb/ft3 |
The Mass velocity is described as,
Gn = Wg / An
Where,
Wg = Mas gas flow, lb/hr |
An = Net free area, ft2 |
And,
An = Ad - do/12 * Lt * Nt
For staggered tubes without corbels,
Ad = ((Nt +0.5) * Pt/12) * Le
For staggered tubes with corbels or inline tubes,
Ad = (Nt * Pt/12) * Le
Where,
Ad = Convection box area, ft2 |
do = Outside tube diameter, in |
Le = Tube length, ft |
Pt = Transverse pitch of tubes, in |
Nt = Number of tubes per row |
We can now use the following script to try some calculations,
Fin Tube Pressure Loss:
For the fin tube pressure drop, we will use the Escoa method.
Dp = ((f+a)*Gn2*Nr)/(rb*1.083E+109)
And,
For staggered layouts,
f = C2 * C4 * C6 * (df/do)0.5
For inline layouts,
f = C2 * C4 * C6 * (df/do)1.0
And,
a = ((1+B2)/(4*Nr))*rb*((1/rout)-(1/rin))
Where,
Dp = Pressure drop, inH2O |
rb = Density of bulk gas, lb/ft3 |
rout = Density of outlet gas, lb/ft3 |
rin = Density of inlet gas, lb/ft3 |
Gn = Mass gas flow, lb/hr-ft2 |
Nr = Number of tube rows |
do = Outside tube diameter, in |
df = Outside fin diameter, in |
And,
B = An / Ad
For staggered tubes without corbels,
Ad = ((Nt +0.5) * Pt/12) * Le
For staggered tubes with corbels or inlune tubes,
Ad = (Nt * Pt/12) * Le
Net Free Area, An:
An = Ad - Ac * Le * Nt
Where,
Ad = Cross sectional area of box, ft2 |
Ac = Fin tube cross sectional area/ft, ft2/ft |
Le = Effective tube length, ft |
Nt = Number tubes wide |
And, |
Ac = (do + 2 * lf * tf * nf) / 12 |
tf = fin thickness, in |
nf = number of fins, fins/in |
Reynolds correction factor, C2:
C2 = 0.07 + 8 * Re-0.45
And,
Re = Gn * do/(12*mb)
Where,
mb = Gas dynamic viscosity, lb/ft-hr |
Geometry correction, C4:
For segmented fin tubes arranged in,
a staggered pattern,
C4 = 0.11*(0.0 5*Pt/do)(-0.7*(lf/sf)^0.23)
an inline pattern,
C4 = 0.08*(0. 15*Pt/do)(-1.1*(lf/sf)^0.20)
For solid fin tubes arranged in,
a staggered pattern,
C4 = 0.11*(0.0 5*Pt/do)(-0.7*(lf/sf)^0.20)
an inline pattern,
C4 = 0.08*(0. 15*Pt/do)(-1.1*(lf/sf)^0.15)
Where,
lf = Fin height, in |
sf = Fin spacing, in |
Non-equilateral & row correction, C6:
For fin tubes arranged in,
a staggered pattern,
C6 = 1.1+(1.8-2.1*e(-0.15*Nr^2))*e(-2.0*Pl/Pt) - (0.7*e(-0.15*Nr^2))*e(-0.6*Pl/Pt)
an inline pattern,
C6 = 1.6+(0.75-1.5*e(-0.70*Nr))*e(-2.0*(Pl/Pt)^2)
Where,
Nr = Number of tube rows |
Pl = Longitudinal tube pitch, in |
Pt = Transverse tube pitch, in |
We can now use the following script to try some calculations,
Stud Tube Pressure Loss:
For the stud tube pressure loss we will use the Muhlenforth method,
The general equation for staggered or inline tubes,
Dp = Nr*0.0514*ns((Cmin-d0-0.8*ls)/((ns*(Cmin-do-1.2*ls)2)0.555))1.8*G2*((Tg+460)/1460)
Where,
Dp = Pressure drop across tubes, inH2O |
Nr = Number of tube rows |
Cmin = Min. tube space, diagonal or transverse, in |
do = Outside tube diameter, in |
ls = Length of stud, in |
G = Mass gass velocity, lb/sec-ft2 |
Tg = Average gas Temperature, °F |
Correction for inline tubes,
Dp = Dp*((do/Cmin)0.333)2
And,
G = Wg/(An*3600)
An = Le*Nt*(Pt-do-(ls*ts*rs)/12)/12
Where,
Wg = Mass flow of gas, lb/hr |
An = Net free area of tubes, ft2 |
Le = Length of tubes, ft |
Nt = Number of tubes wide |
Pt = Transverse tube pitch, in |
ls = Length of stud, in |
ts = Diameter of stud, in |
rs = Rows of studs per foot |
We can now use the following script to try some calculations,