CHEMICAL ENGINEERING

FLOW AND PRESSURE MEASUREMENT 101

Distance from Manometer

duct centre-line (m) Readinghm(mm)

0 104

0.05 100

0.10 96

0.15 86

0.175 79

0.20 68

0.225 50

Calculate the mass flowrate of air through the duct, the average velocity, the ratio of the
average to the maximum velocity and the Reynolds number. Comment on these results.
Discuss the application of this method of measuring gas flowrates, with particular
emphasis on the best distribution of experimental points across the duct and on the accu-
racy of the results.
Take the viscosity of air as 1. 9 ð 10 ^2 mN s/m^2 and the molecular weight of air as
29 kg/kmol.

Solution

Ifhmis the manometer reading, the vertical manometer height will be 0. 1 hm (mm of
water).

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

uD

√

2 gh (equation 6.10)

wherehis the manometer reading in terms of the fluid flowing in the duct.

Thus: hD 0. 1 hm/ 1000 ðw/air

airD 29 / 22. 4  152 / 101. 3  273 / 323 D 1 .64 kg/m^3

∴ hD 0. 1 hm/ 1000  1000 / 1. 64 D 0. 061 hm

and: uD

√

2 ð 9. 81 ð 0. 061 hmD 1. 09

√

hm(m/s)

If the duct is divided into a series of elements with the measured radius at the centre-line
of the element, the velocity of the element can be found from the previous equation and
the volumetric flowrate calculated. By adopting this procedure across the whole section,
the required values may be determined.
For example, at 0.05 m, wherehmD10 mm,
Inner radius of elementD 0 .025 m
Outer radius of elementD 0 .075 m

Area of element D 0. 0752  0. 0252 D 0 .0157 m^2

∴ uD 1. 09

√

hmD 1. 09

p

100 D 10 .9m/s

Volumetric flowrate in the elementD 10. 9 ð 0. 0157 D 0 .171 m^3 /s