CHEMICAL ENGINEERING

FLOW AND PRESSURE MEASUREMENT 97

PROBLEM 6.22

The flowrate of air in a 305 mm diameter duct is measured with a pitot tube which is used
to traverse the cross-section. Readings of the differential pressure recorded on a water
manometer are taken with the pitot tube at ten different positions in the cross-section.
These positions are so chosen as to be the mid-points of ten concentric annuli each of the
same cross-sectional area. The readings are as follows:

Position 1 2 3 4 5
Manometer reading (mm water) 18.5 18.0 17.5 16.8 15.8
Position 6 7 8 9 10
Manometer reading (mm water) 14.7 13.7 12.7 11.4 10.2
The flow is also metered using a 50 mm orifice plate across which the pressure differen-
tial is 150 mm on a mercury-under-water manometer. What is the coefficient of discharge
of the orifice meter?

Solution

For a pitot tube, the velocity at any point in the duct is:

uD

√

2 gh (equation 6.10)

wherehis the manometer reading in m of the fluid which flows in the duct.

∴ hDreading in mm water/ 1000 ðw/airm

The total volumetric air flowrate is given by:

QDarea of ductðaverage velocity

Dareað 1 / 10 

∑√

2 gh

D/ 4 ð 0. 3052 ð 0. 1 ð

√

w/a/ 1000 ð

∑√

manometer reading

D 0. 00102

√

w/a

p

18. 5 C

p

18. 0 C

p

17. 5 CÐÐÐ

p

10. 2 D 0. 0394

√

w/a

For the orifice meter, the volumetric flowrate is given by:

QDCD

A 0

√

1 A 0 /A 1 ^2

√

2 gh

A 0 D/ 4 ð 0. 152 D 0 .0177 m^2 , A 1 D/ 4 ð 0. 3052 D 0 .0731 m^2 , hD50 mm Hg
under water

D 0. 05  13. 6  1. 0 / 1. 0 D 0 .63 m of waterD 0. 63 w/amofair.

∴ QDCDð

0. 0177

√

1  0. 0177 / 0. 0731 ^2

√

2 ð 9. 81 ð 0. 63 w/a

D 0. 066

√

w/aðCD

∴ 0. 0394

p

w/aD 0. 066

p

w/aðCDandCDD 0. 60