Water (dynamic viscosity = 0.01 poise) flows under pressure through a pipe of
10 mm diameter at a velocity of 10 mm /sec. What would be the head loss per
km length of the pipe ? (1 marks )
1.28 m
0.8 m
0.16 m
0.32 m
V
Answers
Shear stress can be expressed
τ = μ dc / dy
= μ γ (1)
where
τ = shearing stress in fluid (N/m2)
μ = dynamic viscosity of fluid (N s/m2)
dc = unit velocity (m/s)
dy = unit distance between layers (m)
γ = dc / dy = shear rate (s-1)
Equation (1) is known as the Newtons Law of Friction.
(1) can be rearranged to express Dynamic viscosity as
μ = τ dy / dc
= τ / γ (1b)
In the SI system the dynamic viscosity units are N s/m2, Pa s or kg/(m s) - where
1 Pa s = 1 N s/m2 = 1 kg/(m s) = 0.67197 lbm/(ft s) = 0.67197 slug/(ft s) = 0.02089 lbf s/ft2
Dynamic viscosity may also be expressed in the metric CGS (centimeter-gram-second) system as g/(cm s), dyne s/cm2 or poise (p) where
1 poise = 1 dyne s/cm2 = 1 g/(cm s) = 1/10 Pa s = 1/10 N s/m2
For practical use the Poise is normally too large and the unit is therefore often divided by 100 - into the smaller unit centipoise (cP) - where
1 P = 100 cP
1 cP = 0.01 poise = 0.01 gram per cm second = 0.001 Pascal second = 1 milliPascal second = 0.001 N s/m2
Water at 20.2oC (68.4oF) has the absolute viscosity of one - 1 - centiPoise.