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Gas Side Pressure Drop Across Tubes

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
Fin Tube Pressure Loss
Stud Tube Pressure Loss


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 inlune 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,
Coil Data
Tube outside dia., in: Tube length, ft:
Number of tubes wide: Number of rows:
Transverse pitch of tubes, in: Corbels:
Process Data
Mass flow, lb/hr: Density of gas, lb/ft3:
Pressure Drop, inHO:
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,
Coil Data
Tube outside dia., in: Tube length, ft:
Number of tubes wide: Number of rows:
Trans. pitch of tubes, in: Long. pitch of tubes, in:
Fin height, in: Fin thickness, in:
Fins density, fins/in: Fin type:
Tube layout: Corbels:
Process Data
Mass flow, lb/hr: Bulk density of gas, lb/ft3:
Inlet density of gas, lb/ft3: Outlet density of gas, lb/ft3:
Bulk viscosity of gas, lb/hr-ft:
Pressure Drop, inH2O:
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,
Coil Data
Tube outside dia., in: Tube length, ft:
Number of tubes wide: Number of rows:
Trans. pitch of tubes, in: Long. pitch of tubes, in:
Stud height, in: Stud diameter, in:
Stud rows per foot: Tube layout:
Process Data
Mass flow, lb/hr: Average gas temperature, °F:
Pressure Drop, inH2O: