CHEMICAL ENGINEERING

FLOW AND PRESSURE MEASUREMENT 81

The coefficient of the diverging coneC^0 Dis given by:

GDC^0 DC^0

√

 2 gh^0 v

h^0 vD 100  15 D85 mm

and: 2. 7 DC^0 Dð 1000 ð 0. 00197 

p

 2 ð 9. 81 ð 0. 085 orC^0 DD 1. 06

PROBLEM 6.5

A venturi meter with a 50 mm throat is used to measure a flow of slightly salt water in
a pipe of inside diameter 100 mm. The meter is checked by adding 20 cm^3 /s of normal
sodium chloride solution above the meter and analysing a sample of water downstream
from the meter. Before addition of the salt, 1000 cm^3 of water requires 10 cm^3 of 0.1 M
silver nitrate solution in a titration. 1000 cm^3 of the downstream sample required 23.5cm^3
of 0.1 M silver nitrate. If a mercury-under-water manometer connected to the meter gives
a reading of 221 mm, what is the discharge coefficient of the meter? Assume that the
density of the liquid is not appreciably affected by the salt.

Solution

If the flow of the solution isxm^3 /s, then a mass balance in terms of sodium chloride
gives:

xð 0. 0585 C 20 ð 10 ^6 ð 58. 5 D 0. 1375  20 ð 10 ^6 Cx

and: xD 0 .0148 m^3 /s

or, assuming the density of the solution is 1000 kg/m^3 , the mass flowrate is:

 0. 0148 ð 1000 D 14 .8 kg/s

For the venturi meter, the area of the throat is given by:

A 1 D/ 4  50 / 1000 ^2 D 0 .00196 m^2

and the area of the pipe is:

A 2 D/ 4  100 / 1000 ^2 D 0 .00785 m^2

From equations 6.32 and 6.33:

C^0 DA 1 A 2 /

√

A^21 A^22 D 0 .00204 m^2

hD221 mm Hgunder-waterD 0. 221  13500  1000 / 1000 D 2 .78 m water

and hence: 14.8 DCDð 1000 ð 0. 00204 

√

 2 ð 9. 81 ð 2. 78 

and: CDD 0. 982