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Section summary |
---|

1. Total pressure
drop on the tube side |

2. Pressure drop
inside the tubes |

3. Calculation of the pressure drop in
inlet and return nozzles |

4. Calculation of the pressure drop in
the return cover |

The pressure drop on the tube 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, the pressure drop in the return cover and the pressure drop through the tubes.

**ΔP _{t} = ΔP_{i} + ΔP_{o}
+ ΔP_{tubes}+ ΔP_{c}**

With

ΔP_{t} = total pressure drop in the heat exchanger (tube
side)

ΔP_{i} = pressure drop in the inlet nozzle

ΔP_{o} = pressure drop in the outlet nozzle

ΔP_{tubes} = pressure drop in the tubes

ΔP_{c} = pressure drop in the return cover

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

ΔP_{tubes} = 2.f.ρ.V^{2}.L_{t}.Φ/d_{i}

With

ΔP_{tubes} = pressure drop in the tubes (Pa)

f = friction factor

ρ = density of the fluid (kg/m3)

V = fluid velocity in tubes (m/s)

L_{t} = total length of flow inside tubes (m)

d_{i} = inside diameter of the tubes (m)

Φ = correction factor for non isothermal flow

The following equation allows to calculate the pressure drop :

**f = 0.0014+0.125*Re ^{-0.32}
(for Re>2100)**

To be noted that the friction factor can be calculated via other correlations, more precise, accessible on Process Engineer's Tools website.

With :

Re = Reynolds number

The fluid velocity in the tubes depends on the number of tubes, the number of passes, the tube diameter and the mass flow of the fluid on the tube sides.

The number of tubes per pass can be calculated the following way :

N_{tp} = N_{t}/n_{t}

The passing area of the fluid is then :

A = N_{tp}*(π.d_{i}^{2}/4)

And the velocity is then :

V = (m/ρ)/A

With

Nt = number of tubes

n_{t} = number of tube passes

N_{tp} = Number of tubes per pass

A = passing section of the fluid (m^{2})

ρ = density of the fluid (kg/m3)

V = fluid velocity in tubes (m/s)

m = mass flowrate of the fluid in the tube side (kg/s)

The total length of flow in the tubes is :

**L _{t} = L*n_{t}**

With

L_{t} = total length of flow in tubes

L = length of tubes

n_{t} = number of tube passes

The correction for non isothermal flow is due to Sieder and Tate and expressed as :

**Φ = (μ/μ _{w})^{-0.25}
in laminar flow**

**Φ = (μ/μ _{w})^{-0.14}
in turbulent flow**

With

μ = viscosity of the fluid at bulk temperature in Pa.s (kg/m/s)

μ_{w} = viscosity of the fluid at the wall temperature in
Pa.s (kg/m/s)

The pressure drop in the nozzles is calculated by :

**ΔP _{i} = 1.5*ρ_{i}*V_{i}^{2}/2**

**ΔP _{o} = 0.5*ρ_{o}*V_{o}^{2}/2**

With :

ΔP_{i} = pressure drop in the inlet nozzle

ΔP_{o} = pressure drop in the outlet nozzle

ρ = density of the fluid (kg/m3) with indice i for inlet and o for
outlet

V = fluid velocity in tubes (m/s) with indice i for inlet and o for
outlet

The pressure drop in the return cover depends on the fluid velocity and the number of passes. It can be calculated by :

ΔP_{c} = (K_{e}.ρ.V^{2})/(2.n_{t})

With :

ΔP_{c} = pressure drop in the return cover

K_{e} = coefficient dependent on the number of passes. 1st
approximation value is 0.9 for 1 tube pass and 1.6 for multi passes
tube

ρ = density of the fluid (kg/m3)

V = fluid velocity in tubes (m/s)

n_{t} = number of tube passes