CHEMICAL ENGINEERING

FLOW AND PRESSURE MEASUREMENT 99

PROBLEM 6.24

Water is flowing through a 100 mm diameter pipe and its flowrate is metered by means
of a 50 mm diameter orifice across which the pressure drop is 13.8kN/m^2. A second
stream, flowing through a 75 mm diameter pipe, is also metered using a 50 mm diameter
orifice across which the pressure differential is 150 mm measured on a mercury-under-
water manometer. The two streams join and flow through a 150 mm diameter pipe. What
would you expect the reading to be on a mercury-under-water manometer connected
across a 75 mm diameter orifice plate inserted in this pipe? The coefficients of discharge
for all the orifice meters are equal. Density of mercuryD13600 kg/m^3.

Solution

As in Problem 6.23:

u^22 D

2 P 1 P 2 v

1 A 1 /A 2 ^2

andQDCDA 2

p

2 P 1 P 2 v

1 A 2 /A 1 ^2

For pipe 1,A 2 D/ 4 ð 0. 052 D 0 .00196 m^2 ,A 1 D/ 4 ð 0. 102 D 0 .00785 m^2 ,

P 1 P 2 D 13 ,800 N/m^2

vD 1 / 1000 D 0 .001 m^3 /kg

∴ Q 1 DCDð 0. 00196

√

2 ð 13 , 800 ð 0. 001

1  0. 00196 / 0. 00789 ^2

D 0. 011 CD

For pipe 2,

p

2 P 1 P 2 vD

p

2 gh (equation 6.10)

A 2 D 0 .00196 m^2 ,A 1 D/ 4 ð 0. 0752 D 0 .0044 m^2

Head loss, hD150 mm Hg-under-water or  150 / 1000 ð[ 13 , 600  1000 /1000]
D 1 .89 m water.

∴ Q 2 DCDð 0. 00196

√

2 ð 9. 81 ð 1. 89

1  0. 00196 / 0. 0044 ^2

D 0. 0133 CD

Total flow in pipe 3,Q 3 DQ 1 CQ 2 D 0. 011 CDC 0. 0133 CDD 0. 0243 CD

For pipe 3,A 2 D/ 4 ð 0. 0752 D 0 .0044 m^2 ,A 1 D/ 4 ð 0. 152 D 0 .0176 m^2

and: Q 3 DCDð 0. 0044

√

2 ð 9. 81 ðh

 1  0. 0044 / 0. 0176 ^2 

D 0. 020 CD

p

h

∴ 0. 0243 CDD 0. 020 CD

p

h

and: hD 1 .476 m of water

or  1. 476 ð 1000 / 13600  1000 / 1000 D117 mm of Hg-under-water.