 # Shell - Tube Heat Exchanger : pressure drop on the shell side

## How to calculate the pressure drop in the shell of a shell-tube HX ?

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1. Heat transfer on the tube side of a shell tube heat exchanger
2. Calculation of the heat transfer coefficient on the tube side

## 1. Total pressure drop on the shell side

The pressure drop on the shell side of a shell-tubes heat exchanger is made of several components : the pressure drop in the inlet nozzle, the pressure drop in the outlet nozzle and the pressure drop through the tube bundle in the shell.

ΔPt = ΔPi + ΔPo + ΔPs

With

ΔPt = total pressure drop in the heat exchanger (shell side)
ΔPi = pressure drop in the inlet nozzle
ΔPo = pressure drop in the outlet nozzle
ΔPs = pressure drop in the shell

The most complex is to calculate the pressure drop in the shell.

## 2. Pressure drop inside the shell

### How to calculate the pressure drop inside the shell of a shell-tubes heat exchanger ?

The Bell Delaware method expresses the pressure drop inside the shell with the following formula :

ΔPs = [(Nch-1).ΔPCTKBP+Nch.ΔPCF].KF+2.ΔPCTKBP.(1+NOF/NCT)

With

ΔPs = pressure drop in the shell (Pa)
Nch = number of baffles
ΔPCT = pressure drop in between 2 baffles for ideal cross flow (Pa)
ΔPCF = pressure drop in the baffle window section (Pa)
KBP = correction factor for bypass flow
KF = correction factor for leakage in between shell / baffles and tubes / baffles
NOF = number of tubes in baffle window
NCT = Number of tube rows crossed between baffle tips in one baffle section

### 2.1 Pressure drop ΔPCT in cross flow in between 2 baffles

The following equation allows to calculate the pressure drop :

Nu = 1.86.Re1/3.Pr1/3.(di / L)1/3.(μ/μt)0.14 With :

Re = Reynolds number
Pr = Prandtl number = Cp.μ / λ
di = internal diameter of the tube in m
L = length of the tube in m
μ = viscosity of the fluid at bulk temperature in Pa.s (kg/m/s)
μt = viscosity of the fluid a wall temperature in Pa.s (kg/m/s)
Cp = specific heat of the fluid in J/kg/K (m2/s2/K)
λ = thermal conductivity of the fluid (W/(m.K)) (m⋅kg⋅s−3⋅K−1)

### 2.2 Turbulent flow (Re > 10000)

The following correlation is from Colburn.

Nu = 0.027.Re0.8.Pr1/3.(μ/μt)0.14 ### 2.3 Calculation of Reynold number

The Reynolds number can be calculated as a function of the mass flow, number of tubes, number of passes, tube diameter.

Re = G.di / μ

G = m / [(Nt/nt).π.di2/4] With

G = mass flux in the tube in kg/s/m2
ṁ = mass flow in the heat exchanger on the tube side in kg/s
Nt = number of tubes in the shell tube heat exchanger
nt = number of passes tube in the shell tube heat exchanger
μ = viscosity of the fluid at bulk temperature in Pa.s (kg/m/s)