CHEMICAL ENGINEERING

SECTION 3

Flow in Pipes and Channels

PROBLEM 3.1

Calculate the hydraulic mean diameter of the annular space between a 40 mm and a
50 mm tube.

Solution

The hydraulic mean diameter,dm, is defined as four times the cross-sectional area divided
by the wetted perimeter. Equation 3.69 gives the valuedmfor an annulus of outer radius
rand inner radiusrias:

dmD 4 r^2 ri^2 / 2 rCriD 2 rriDddi

IfrD25 mm andriD20 mm, then:

dmD 2  25  20 D10 mm

PROBLEM 3.2

0.015 m^3 /s of acetic acid is pumped through a 75 mm diameter horizontal pipe 70 m
long. What is the pressure drop in the pipe?
Viscosity of acidD 2 .5mNs/m^2 , density of acidD1060 kg/m^3 , and roughness of pipe
surfaceD 6 ð 10 ^5 m.

Solution

Cross-sectional area of pipeD/ 4  0. 075 ^2 D 0 .0044 m^2.

Velocity of acid in the pipe,uD 0. 015 / 0. 0044 D 3 .4m/s.

Reynolds numberDud/ D 1060 ð 3. 4 ð 0. 07 / 2. 5 ð 10 ^3 D 1. 08 ð 105

Pipe roughnesseD 6 ð 10 ^5 mande/dD 6 ð 10 ^5 / 0. 075 D 0. 0008

The pressure drop is calculated from equation 3.18 as:PfD 4 R/u^2 l/du^2 

From Fig. 3.7, whenReD 1. 08 ð 105 ande/dD 0 .0008,R/u^2 D 0 .0025.

Substituting:PfD 4 ð 0. 0025  70 / 0. 075  1060 ð 3. 42 
D 114 ,367 N/m^2 or: 114.4kN/m^2

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