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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:

Heat Exchanger Tube Pressure Drop Calculation, Online Calculator

Intube Pressure Drop




The intube pressure drop may be calculated by any number of methods available today, but the following procedures should give sufficient results for heater design. The pressure loss in heater tubes and fittings is normally calculated by first converting the fittings to an equivalent length of pipe. Then the average properties for a segment of piping and fittings can be used to calculate a pressure drop per foot to apply to the overall equivalent length. This pressure drop per foot value can be improved by correcting it for inlet and outlet specific volumes.






Friction Loss:







D_p = 0.00517/d_i*G²*V_lm*F*L_equiv


Where,

Dp = Pressure drop, psi

di = Inside diameter of tube, in

G = Mass velocity of fluid, lb/sec-ft2

Vlm = Log mean specific volume correction

F = Fanning friction factor

Lequiv = Equivalent length of pipe run, ft

And,









V_lm = (V₂-V₁)/ln(V₂/V₁)


For single phase flow,

V1 = Specific volume at start of run, ft3/lb

V2 = Specific volume at end of run, ft3/lb

For mixed phase flow,









V_i = 10.73*(T_f/(P_v*MW_v)*V_frac+(1-V_frac)/r_l


Where,

Vi = Specific volume at point, ft3/lb

Tf = Fluid temperature, °R

Pv = Press. of fluid at point, psia

MWv = Molecular weight of vapor

Vfrac = Weight fraction of vapor %/100

rl = Density of liquid, lb/ft3

Fanning Friction Factor:




The Moody friction factor, for a non-laminar flow, may be calculated by using the Colebrook equation relating the friction factor to the Reynolds number and relative roughness. And the Fanning friction factor is 1/4 the Moody factor. For a clean pipe or tube, the relative roughness value for an inside diameter given in inches is normally 0.0018 inch.




With this, we can calculate the factor,

Reynolds number =
Inside Diameter, inches =

Friction factor, F:

Equivalent Length Of Return Bends:




The equivalent length of a return bend may be obtained from the following curves based on Maxwell table and can be corrected using the Reynolds number correction factor.







L_equiv = Fact_Nre*L_rb


Where,

FactNre = Reynolds number correction

Lrb = Equivalent length of return bend, ft

Return Bend Equivalent Length:

Reynolds Correction:

Where,

G = Mass velocity, lb/sec-ft2

Di = Inside tube diameter, in

Visc = Viscosity, cp

Now that we have all the details described, we can calculate the pressure drop for some typical heater coils.

Coil Data
Tube inside dia., in:	Pipe straight length, ft:
Bend radius, in:	Number of returns:
Process Data
Mass vel., lb/sec-ft2:	Viscosity, cp:
Spec. vol. at start, ft3/lb:	Spec. vol. at end, ft3/lb:

 Pressure Drop, psi:

Online Heat Transfer Coefficient Calculator

Heat Transfer Coefficients


The inside film coefficient needed for the thermal calculations may be estimated by several different methods. The API RP530, Appendix C provides the following methods,

For liquid flow with R_e =>10,000,




h_l = 0.023(k/d_i)R_e^0.8*P_r^0.33(m_b/m_w)^0.14

And for vapor flow with R_e =>15,000,




h_v = 0.021(k/d_i)R_e^0.8*P_r^0.4(T_b/T_w)^0.5

Where the Reynolds number is,




R_e = d_i*G/m_b

And the Prandtl number is,




P_r = C_p*m_b/k

Where,

hl = Heat transfer coefficient, liquid phase, Btu/hr-ft2-°F

k = Thermal conductivity, Btu/hr-ft-°F

di = Inside diameter of tube, ft

mb = Absolute viscosity at bulk temperature, lb/ft-hr

mw = Absolute viscosity at wall temperature, lb/ft-hr

hv = Heat transfer coefficient, vapor phase, Btu/hr-ft2-°F

Tb = Bulk temperature of vapor, °R

Tw = Wall Temperature of vapor, °R

G = Mass flow of fluid, lb/hr-ft2

Cp = Heat capacity of fluid at bulk temperature, Btu/lb-°F

For two-phase flow,



h_tp = h_lW_l + h_vW_v

Where,

htp = Heat transfer coefficient, two-phase, Btu/hr-ft2-°F

Wl = Weight fraction of liquid

Wv = Weight fraction of vapor

The following script will allow us to try these formulas out using our browser.

Tube diameter, in:		Mass flow, lb/hr-ft2:
Percent vapor, %:		Bulk Temp., °F:
Liquid Properties		Vapor Properties
Thermal cond., Btu/hr-ft-°F:		Thermal cond., Btu/hr-ft-°F:
Visc. bulk, lb/ft-hr:		Visc. bulk, lb/ft-hr:
Spec. Heat, Btu/lb-°F:		Spec. Heat, Btu/lb-°F:
Visc. @ wall, lb/ft-hr:		Temp. @ wall, °F:

h_l Coefficient, Btu/hr-ft²-°F:


h_v Coefficient, Btu/hr-ft²-°F:


h_tp Coefficient, Btu/hr-ft²-°F:


Reynolds number:LiquidVapor

It should be stressed at this time, that there are many ways to calculate the inside heat transfer coefficient, and a lot of care should be taken in the procedure selected for use in heater design. Other methods, such as HTRI, Maxwell, Dittus-Boelzer, or others may be more appropriate for a particular heater design.