How to know a pipe is partially full ?

What is the liquid height and equivalent diameter ?

1. Introduction
2. Pipe full or partially filled ?
3. Height of liquid in the pipe calculation
4. Equivalent diameter calculation

1. Introduction

It happens that pipes are not actually full, for example in some return pipes, condensate...etc... then the assumption that they are full can lead to some erroneous calculations. [Brannan] is reporting a method proposed by Durand in order to know if a pipe is totally full or not.

2. Pipe full or partially filled ?

To know if the pipe is full or not, it is necessary to calculate Q/d2.5
- If ≥ 10.2 it means the pipe is full
- If < 10.2 the pipe may be partially full only, further calculations are required to know the height of liquid in the pipe and the equivalent diameter

With :
Q = flow rate in gpm
d = pipe diameter in in

3. Height of liquid

The method is proposing to have x = ln (Q/d2.5)

Then calculate H/D = 0.446+0.272x+0.0397x2-0.0153x3-0.003575x4

With :
H = height of liquid in the pipe in ft

4. Equivalent diameter calculation

The equivalent diameter can be calculated from the following correlation :

De/D = -0.01130+3.040 (H/D) -3.461 (H/D)2 +4.108 (H/D)3 -2.638 (H/D)4

With :
D = pipe diameter in ft
De = equivalent diameter in ft

Rules of thumb for Chemical Engineers, Brannan, Elsevier, page 5


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