CHEMICAL ENGINEERING

FLOW AND PRESSURE MEASUREMENT 91

PROBLEM 6.16

The flowrate of air at 298 K in a 0.3 m 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:

Position 1 2 3 4 5

Manometer reading (mm water) 18.5 18.0 17.5 16.8 15.7

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 150 mm orifice plate across which the pressure
differential is 50 mm on a mercury-under-water manometer. What is the coefficient of
discharge of the orifice meter?

Solution

Cross-sectional area of ductD/ 4  0. 3 ^2 D 0 .0707 m^2.

Area of each concentric annulusD 0 .00707 m^2.
If the diameters of the annuli are designatedd 1 ,d 2 etc., then:

0. 00707 D/ 4  0. 32 d^21 

0. 00707 D/ 4 d^2 d^22 

0. 00707 D/ 4 d^22 d^23 andsoon,

and the mid-points of each annulus may be calculated across the duct.

For a pitot tube, the velocity may be calculated from the headhasuD

p

 2 gh

For position 1,hD 18 .5mmofwater.

The density of the airD 29 / 22. 4  273 / 298 D 1 .186 kg/m^3.

hD 18. 5 ð 10 ^3 ð 1000 / 1. 186 D 15 .6mofair

and: uD

√

 2 ð 9. 81 ð 15. 6 D 17 .49 m/s

In the same way, the velocity distribution across the tube may be found as shown in
the following table.

Mass flowrate,GD 1. 107 ð 1. 186 D 1 .313 kg/s

For the orifice, [1A 0 /A 1 ^2 ]D[1 0. 15 / 0. 3 ^2 ]D 0. 938

hD50 mm Hg-under-water

D 0. 05 ð 13. 55  1 ð 1000 / 1. 186 D529 m of air

and: 1. 313 DCD/ 4  0. 15 ^2 ð 1. 186

p

 2 ð 9. 81 ð 529 / 0. 938 andCDD 0. 61