CHEMICAL ENGINEERING

FLOW AND PRESSURE MEASUREMENT 79

PROBLEM 6.3

Water flows at between 3 l and 4 l/s through a 50 mm pipe and is metered by means of
an orifice. Suggest a suitable size of orifice if the pressure difference is to be measured
with a simple water manometer. What is the approximate pressure difference recorded at
the maximum flowrate?

Solution

Equations 6.19 and 6.21 relate the pressure drop to the mass flowrate. If equation 6.21 is
used as a first approximation,GDCDA 0 

p
 2 gh.
For the maximum flow of 4 l/s,GD4 kg/s. The largest practicable height of a water
manometer will be taken as 1 m and equation 6.21 is then used to calculate the orifice
areaA 0. If the coefficient of dischargeCDis taken as 0.6, then:

4. 0 D 0. 6 A 0 ð 1000

√

 2 ð 9. 81 ð 1. 0 ,A 0 D 0 .0015 m^2 andd 0 D 0 .0438 m

The diameter,d 0 , is comparable with the pipe diameter and hence the area correction
term must be included and:

[1A 0 /A 1 ^2 ]D[1 43. 82 / 502 ^2 ]D 0. 641.

Therefore the value ofA 0 must be recalculated as:

4. 0 D 0. 6 A 0 ð 1000

√

 2 ð 9. 8 ð 1. 0 /[1A 0 /A 1 ^2 ]

from whichA 0 D 0 .00195 m^2 anddD 0 .039 m or 39 mm

√

[1A 0 /A 1 ^2 ]D

√

[1 392 / 502 ^2 ]D 0. 793

Substituting in equation 6.19:

4. 0 D 0. 6 ð 0. 00195 ð 1000

√

 2 ð 0. 001 P/ 0. 793 

and: PD12320 N/m^2 or 12.3kN/m^2

PROBLEM 6.4

The rate of flow of water in a 150 mm diameter pipe is measured by means of a venturi
meter with a 50 mm diameter throat. When the drop in head over the converging section
is 100 mm of water, the flowrate is 2.7 kg/s. What is the coefficient for the converging
cone of the meter at that flowrate and what is the head lost due to friction? If the total loss
of head over the meter is 15 mm water, what is the coefficient for the diverging cone?