CHEMICAL ENGINEERING

FLOW AND PRESSURE MEASUREMENT 85

be the reading on a mercury-under-water manometer connected to the meter? What is the
Reynolds number for the flow in the pipe? Density of waterD1000 kg/m^3. Viscosity of
waterD1mNs/m^2.

Solution

Mass flowrate,GD 1500 ð 10 ^6 ð 1000 D 1 .5 kg/s.

Area of orifice,A 0 D/ 4  0. 025 ^2 D 0 .00049 m^2.

Area of pipe,A 1 D/ 4  0. 050 ^2 D 0 .00196 m^2.

Reynolds numberDud/ DdG/A 1 /
D 0. 05  1. 5 / 0. 00196 / 1 ð 10 ^3 D 3. 83 ð 104

The orifice meter equations are 6.19 and 6.21; the latter being used when

√

[1A 0 /A 1 ^2 ]

approaches unity.

Thus:

√

[1A 0 /A 1 ^2 ]D

√

[1 252 / 502 ^2 ]D 0. 968

Using equation 6.21,GDCDA 0 

p

 2 ghgives:

1. 5 D 0. 62 ð 0. 00049 ð 1000

√

 2 ð 9. 81 h, andhD 1 .24 m of water

Using equation 6.19 in terms ofhgives:

1. 5 D 0. 62 ð 0. 00049 ð 1000 / 0. 968 

√

 2 ghandhD 1 .16 m of water

This latter value ofhshould be used. The height of a mercury-under-water manometer
would then be 1. 16 / 13. 55  1. 00 / 1. 00 D 0 .092mor 92mmHg.

PROBLEM 6.10

What size of orifice would give a pressure difference of 0.3 m water gauge for the flow
of a petroleum product of density 900 kg/m^3 at 0.05 m^3 /s in a 150 mm diameter pipe?

Solution

As in previous problems, equations 6.19 and 6.21 may be used to calculate the flow
through an orifice. In this problem the size of the orifice is to be found so that the simpler
equation will be used in the first instance.

GDCDA 0 

√

 2 gh (equation 6.21)

GD 0. 05 ð 900 D 45 .0 kg/s

D900 kg/m^3