CHEMICAL ENGINEERING

98 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

PROBLEM 6.23

The flow of liquid in a 25 mm diameter pipe is metered with an orifice meter in which the
orifice has a diameter of 19 mm. The aperture becomes partially blocked with dirt from
the liquid. What fraction of the area can become blocked before the error in flowrate at a
given pressure differential exceeds 15 per cent? Assume that the coefficient of discharge
of the meter remains constant when calculated on the basis of the actual free area of the
orifice.

Solution

If two sections in the pipe are chosen, 1 being upstream and 2 at the orifice, then from
an energy balance:

u^21 / 2 CP 1 vDu^22 / 2 CP 2 v (from equation 2.55)

andG,themassflowrateDu 2 A 2 /vDu 1 A 1 /v

∴ u^22 / 2 A 2 /A 1 ^2 CP 1 vDu^22 / 2 CP 2 v

or: u^22 D

2 P 1 P 2 v

1 A 2 /A 1 ^2

The volumetric flowrate,QDCDA 2 u 2

∴ Q^2 DC^2 DA^22 ð

2 P 1 P 2 v

1 A 2 /A 1 ^2

D 2 C^2 DP 1 P 2 vA^21 A^22 /A^21 A^22 

or: QDK

A 1 A 2

√

A^21 A^22

 1 

If the area of the orifice is reduced by partial blocking, the new orifice areaDrA 2
wherefis the fraction available for flow. The new flowrateD 0. 85 Qwhen the error is
15 per cent and:

0. 85 QD

KA 1 fA 2

√

A^21 f^2 A^22

 2 

A 1 D/ 4 ð 252 D491 mm^2

A 2 D/ 4 ð 192 D284 mm^2

∴Dividing equation (2) by equation (1) and substituting gives:

0. 85 D

f

√

 4912  2842 

√

 4912 r^22842 

from whichfD 0 .89 or 11 per centof the area is blocked.