9.1 Basic Concepts and Formulae
393
Fig. 9.1
The pitot tube is a device to measure the flow speed of a gas. If ρ is the density of
the liquid in the manometer, ρ the density of the flowing gas and h the difference in
height in the limbs of the manometer, then
v =
2ghρ
ρ
(9.10)
Viscosity: The coefficient of viscosity of a liquid is the tangential force per unit
area per unit velocity gradient. The backward tangential force acting on any liquid
layer is
F = −η A
dv
dy
(9.11)
where dv/dy is the velocity gradient which is identical with v/y for constant gradient. The negative sign shows that the viscous drag acts opposite to the velocity of
the liquid.
Poiseuille’s Method for Viscosity Determination
Volume V flowing per second through a tube of radius a and length L under pressure
head P is given by
V =
π Pa 4
8ηL
(9.12)
Terminal velocity
Drag force F = 6πηr v (Stokes law)
(9.13)
When a sphere of radius r and of density ρ 0 is dropped in an extensive fluid of
density ρ its speed increases linearly as for a free fall (v = gt). However, due to
viscous drag v approaches asymptotically to a constant value v T given by
v T =
2gr 2
9η
(ρ 0 − ρ)
(9.14)