Heater Design: Gas Side Pressure Drop Across Tubes, Online Calculation

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

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Bare Tube Pressure Loss:


For bare tubes we can use the method presented by Winpress(Hydrocarbon Processing, 1963),


D_p = P_v /2 * N_r


Where,

Dp = Pressure drop, inH2O

Pv = Velocity head of gas, inH2O

Nr = Number of tube rows

And the velocity head can be described as,


P_v = 0.0002307 * (G_n /1000)² / r_g


Where,

Gn = Mass velocity of gas, lb/hr-ft2

rg = Density of gas, lb/ft3

The Mass velocity is described as,



G_n = W_g / A_n
Where,

Wg = Mas gas flow, lb/hr

An = Net free area, ft2

And,



A_n = A_d - d_o/12 * L_e * N_t


For staggered tubes without corbels,



A_d = ((N_t +0.5) * P_t/12) * L_e


For staggered tubes with corbels or inline tubes,



A_d = (N_t * P_t/12) * L_e


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: Yes No
Process Data
Mass flow, lb/hr:	Density of gas, lb/ft3:

Pressure Drop, inH2O:

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Fin Tube Pressure Loss:


For the fin tube pressure drop, we will use the Escoa method.





D_p = ((f+a)*G_n²*N_r)/(r_b*1.083E+10⁹)


And,
For staggered layouts,


f = C₂ * C₄ * C₆ * (d_f/d_o)^0.5
For inline layouts,


f = C₂ * C₄ * C₆ * (d_f/d_o)^1.0


And,



a = ((1+B²)/(4*N_r))*r_b*((1/r_out)-(1/r_in))


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 = A_n / A_d


For staggered tubes without corbels,


A_d = ((N_t +0.5) * P_t/12) * L_e


For staggered tubes with corbels or inlune tubes,


A_d = (N_t * P_t/12) * L_e


Net Free Area, A_n:


A_n = A_d - A_c * L_e * N_t


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 * R_e^-0.45


And,


R_e = G_n * d_o/(12*m_b)


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*P_t/d_o)^{(-0.7*(lf/sf)^0.23)}







an inline pattern,
C₄ = 0.08*(0. 15*P_t/d_o)^{(-1.1*(lf/sf)^0.20)}


For solid fin tubes arranged in,



a staggered pattern,
C₄ = 0.11*(0.0 5*P_t/d_o)^{(-0.7*(lf/sf)^0.20)}




an inline pattern,
C₄ = 0.08*(0. 15*P_t/d_o)^{(-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: Segmented Solid
Tube layout: Staggered Inline	Corbels: Yes No
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:

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Stud Tube Pressure Loss:
For the stud tube pressure loss we will use the Muhlenforth method,
The general equation for staggered or inline tubes,





D_p = N_r*0.0514*n_s((C_min-d₀-0.8*l_s)/((n_s*(C_min-d_o-1.2*l_s)²)^0.555))^1.8*G²*((T_g+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,



D_p = D_p*((d_o/C_min)^0.333)²


And,



G = W_g/(A_n*3600)





A_n = L_e*N_t*(P_t-d_o-(l_s*t_s*r_s)/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: Staggered Inline
Process Data
Mass flow, lb/hr:	Average gas temperature, °F:

Pressure Drop, inH₂O: