An Empirical Approach for Calculating The Pressure Drop in Pneumatic Transport

The pressure loss for pure gas flow in a pipe of length Dl is

DP =

подпись: dp =(14.87)

Where D is the diameter of the pipe. The pipe friction coefficient Af; can be calculated from

AG = 0.3164 Re"1/4 (14.88)

For Reynolds numbers 2320 < Re < 105, or from

L/JTG = 2.0 log10(Re7v;)-0.8, (14.89)

VD

подпись: vd

Re =

подпись: re =

(14.90)

подпись: (14.90)

Where V is the kinematic viscosity of the gas.

For calculating the pressure loss in pneumatic transport, the following simply modified version of Eq. (14.87) is often presented in the literature:

подпись: where v is the kinematic viscosity of the gas.
for calculating the pressure loss in pneumatic transport, the following simply modified version of eq. (14.87) is often presented in the literature:
Which is valid for fully turbulent flow. The Reynolds number is defined by

Equation (14.91) contains only the mass flow ratio Jx as a characteristic number of the mechanics of similitude of the mixture. All the other impor­tant factors, such as particle size, solid density, etc., are contained in the ad­ditional pressure-loss coefficient of the solid particles, s, which is determined separately for each material.

But how can we estimate the pressure-loss coefficient A5? Stegmaierl~ has summarized horizontal transport for several fine-granular solids by a correla­tion which contains some characteristics of the material. The same idea has been used by Weber,13 who has found a correlation of the pressure-loss coeffi­cient for vertical pneumatic conveyance based on data measured by Flatow.14 In order to express these models, we first introduce two dimensionless numbers

Fr = (14.921

Dg

And

Fr, = ^5Q, ! 14.931

Asg

Where g is the acceleration due to gravity (9.82 m/s2) and Ws0 is the free-fall­ing velocity of a solid particle of diameter Ds. The numbers Fr and Fr, are called Froude numbers related to the pipe and solids, respectively.

The mathematical model developed by Stegmaier for horizontal transport

Is

1,- 0.25

2.1 /x ’Fr Fr

O. i

 

An Empirical Approach for Calculating The Pressure Drop in Pneumatic Transport

(14.94)

 

Equation (14.94) is an average value for the most solids. This has a rather high standard deviation, which can be seen from Fig. 14.13.

If the relatively high standard deviation is not acceptable, each type of solid can be correlated separately. This is a standard approach in the literature but we shall not repeat it here.

It is known from experience with vertical pneumatic transport that the in­fluence of weight prevails at low velocities, but as the velocity increases fric­tion gains importance. Therefore, in the calculation of the pressure loss one must find not only the weight of the solids, which could be set up theoreti­cally, but also an empirical relationship for vertical transport from the mea­sured data. A correlation of the pressure-loss coefficient for vertical pneumatic conveyance according to data measured by Flatow14 has been developed by Weber,13 and the result is

1 _ V/c , Iv/c _ (14.95)

1200 Fr

The correlation of Eq. (14.95) with Flatow’s measurements is rather good, as shown in Fig. 14.14. Its standard deviation is about 15%.

Symbol

Solid

Ds

(mm)

Ps

Kg/m3

D

(mm)

Ref.

Totalit

40

2200

40

Bohnet

*

Sand

69

2650

8

Bohnet

D

Quarzpowder

15

2640

70

Miiller

О

Catalyst

70

1500

8

Bohnet

О

Sand

6У

2650

40

Bohnet

Catalyst

70

1500

40

Bohnet

V

Flyash

24

2360

40

Bohnet

Д

Totalit

40

2200

8

Bohnet

О

Alumina

45

2480

40

Lippert

*

Ferrous sulfate waste

112

4100

40

Lippert

Ferrous sulfate waste

46

4100

40

Lippert

1F.+0 I

подпись: 1f.+0 i

IE+00

подпись: ie+00

IE-02

подпись: ie-02

IE-03

подпись: ie-03 An Empirical Approach for Calculating The Pressure Drop in Pneumatic Transport

D,(mm)

D (mm)

+ Polystrole

1/2.7

50/100/200

0.5/27

Glass

Spheres

1.21

50/100/200

0.5/19

Ф Steel spheres

1.13

50/100/200

0.5/12

An Empirical Approach for Calculating The Pressure Drop in Pneumatic Transport

5 10 50

VFr

■ FIGURE 14.14 Correlation of the pressure loss coefficient for vertical pneumatic conveyance based on Flatow’s data according to Weber.13

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