CHEMICAL ENGINEERING

96 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

The specific volume,vD 22. 4 / 44  373 / 273  101. 3 / 202. 6 D 0 .348 m^3 /kg

∴ u 1 D

p

2 ð 373. 8 ð 0. 348 D 16 .1m/s

PROBLEM 6.21

Glycerol, of density 1260 kg/m^3 and viscosity 50 mNs/m^2 , is flowing through a 50 mm
pipe and the flowrate is measured using an orifice meter with a 38 mm orifice. The
pressure differential is 150 mm as indicated on a manometer filled with a liquid of the
same density as the glycerol. There is reason to suppose that the orifice meter may have
become partially blocked and that the meter is giving an erroneous reading. A check is
therefore made by inserting a pitot tube at the centre of the pipe. It gives a reading of
100 mm on a water manometer. What does this suggest?

Solution

From the reading taken from the pitot tube, the velocity in the pipe, and hence the
mass flowrate, can be calculated. From the orifice meter, the mass flowrate can also be
calculated and compared with the accurate value.

For the pitot tube,uD

√

2 gh (equation 6.10)

whereuDumaxat the pipe axis, and the head losshis in m of the liquid flowing.

Now: hD 100 / 1000 ð 1000 / 1260 D 0 .0794 m of glycerol

∴ umaxD

p

2 ð 9. 81 ð 0. 0794 D 1 .25 m/s

Reynolds numberD 1260 ð 1. 25 ð 0. 05 / 0. 05 D 1575

∴ uavD 0. 5 umaxD 0 .63 m/s (equation 3.36)

Mass flowrateD 0. 63 ð 1260 ð/ 4 ð 0. 052 D 1 .56 kg/s

For the orifice meter:

mass flowrate,GDCD

A 0

v

√

2 vP 1 P 2 

1 A 0 /A 1 ^2

(equation 6. 19 

DCDA 0 

√

2 gh

1 d 0 /d^4

DCDð/ 4 ð 0. 0382 ð 1260 

√

2 ð 9. 81 ð 150 / 1000 

1  0. 038 / 0. 05 ^4

D 2. 99 CD

∴CDD 1. 56 / 2. 99 D 0 .53 which confirms that the meter is faulty.