CHEMICAL ENGINEERING

80 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Solution

The equation relating the mass flowrateGand the head loss across a venturi meter is
given by:

GD

CDA 0

v

√

2 vP 1 P 2 

1 A 0 /A 1 ^2

(equation 6.19)

GDCD

A 1 A 2

√

A^21 A^21 

√

 2 vP 1 P 2  (equation 6.32)

GDCDC^0

√

 2 ghv (equation 6.33)

whereC^0 is a constant for the meter andhvis the loss in head over the converging cone
expressed as height of fluid.

A 1 D/ 4  0. 15 ^2 D 0 .0176 m^2

A 2 D/ 4  0. 05 ^2 D 0 .00196 m^2

C^0 D 0. 0176 ð 0. 00196 /

√

 0. 01762  0. 001962 D 0 .00197 m^2

hvD 0 .1m

∴ 2. 7 DCDð 1000 ð 0. 00197 

p

 2 ð 9. 81 ð 0. 10 andCDD 0. 978

In equation 6.33, if there were no losses, the coefficient of discharge of the meter would
be unity, and for a flowrateGthe loss in head would behvhfwherehfis the head
loss due to friction.

Thus: GDC^0

√

[2ghvhf]

Dividing this equation by equation 6.33 and squaring gives:

1 hf/hvDC^2 DandhfDhv 1 C^2 D

∴ hfD 100  1  0. 9782 D 4 .35 mm

If the head recovered over the diverging cone ish^0 vand the coefficient of discharge for
the converging cone isC^0 D,thenGDC^0 DC^0

√

 2 gh^0 v
If the whole of the excess kinetic energy is recovered as pressure energy, the coefficient
C^0 Dwill equal unity andGwill be obtained with a recovery of head equal toh^0 vplus some

quantityh^0 f,GDC^0

√

[2gh^0 vCh^0 f

Equating these two equations and squaring gives:

C

(^02)
DD^1 Ch
0
f/h
0
vandh
0
fDh
0
vC
(^02)
D^1 
Thus the coefficient of the diverging cone is greater than unity and the total loss of
headDhfCh^0 f.
Head loss over diverging coneD 15. 0  4. 35 D 10 .65 mm