FLOW IN PIPES AND CHANNELS 39
From equation 3.8,PD 4 R/ u^2 l/d u^2
D 4 ð 0. 0027 ð 1200 ð 950 ð 2. 042 / 0. 5
D 1. 03 ð 105 N/m^2
R/ u^2 Re^2 DPd^3 / 4 l ^2 (equation 3.23)
D 1. 03 ð 105 ð 0. 53 ð 980 / 4 ð 1200 ð 0. 022 D 6. 6 ð 106From Fig. 3.8,ReD 4. 2 ð 104 D 980 uð 0. 5 / 0. 02
and: uD 1 .71 m/s
∴ volumetricflowrateD 1. 71 ð 0. 196 D 0 .34 m^3 /s
PROBLEM 3.26
Water (density 1000 kg/m^3 , viscosity 1 mNs/m^2 ) is pumped through a 50 mm diameter
pipeline at 4 kg/s and the pressure drop is 1 MN/m^2. What will be the pressure drop for
a solution of glycerol in water (density 1050 kg/m^3 , viscosity 10 mNs/m^2 ) when pumped
at the same rate? Assume the pipe to be smooth.
Solution
Cross-sectional area of pipeD/ 4 ð 0. 052 D 0 .00196 m^2
Water velocity,uD 4 / 1000 ð 0. 00196 D 2 .04 m/s.
Reynolds number,ReD 2. 04 ð 1000 ð 0. 05 / 1 ð 10 ^3 D 102 , 000
From Fig. 3.7,R/ u^2 D 0. 0022
From equation 3.18,PD 4 ð 0. 0022 ðl/ 0. 05 ð 1000 ð 2. 042 D 732 l
For glycerol/waterflowing at the same velocity:
ReD 2. 4 ð 1050 ð 0. 05 / 1 ð 10 ^2 D 10 , 700From Fig. 3.7, R/ u^2 D 0. 0037
and: PD 4 ð 0. 0037 ðl/ 0. 05 ð 1050 ð 2. 042 D 1293 l.
∴ Pglycerol/PwaterD 1293 l/ 732 /lD 1. 77
and PglycerolD 1. 77 ð 1 ð 106 D 1. 77 ð 106 N/m^2
PROBLEM 3.27
A liquid is pumped in streamlineflow through a pipe of diameterd.Atwhatdistance
from the centre of the pipe will thefluid beflowing at the average velocity?