Water is flowing through a pipe of diameter 30 cm at a velocity of 4 m/s. Find the velocity of oil flowing in another pipe of diameter 10 cm, if the condition of dynamic similarly is satisfied between the two pipes. The viscosity of water and oil is given as 0.01 poise and 0.025 poise. The sp gravity of oil is 0.8
Answers
Explanation:
Molecules of fluids exert forces of attraction on each other. In liquids this is strong enough to keep the
mass together but not strong enough to keep it rigid. In gases these forces are very weak and cannot hold
the mass together.
When a fluid flows over a surface, the layer next to the surface may become attached to it (it wets the
surface). The layers of fluid above the surface are moving so there must be shearing taking place between
the layers of the fluid.
Fig.1.1
Let us suppose that the fluid is flowing over a flat surface in laminated layers from left to right as shown
in figure 1.1.
y is the distance above the solid surface (no slip surface)
L is an arbitrary distance from a point upstream.
dy is the thickness of each layer.
dL is the length of the layer.
dx is the distance moved by each layer relative to the one below in a corresponding time dt.
u is the velocity of any layer.
du is the increase in velocity between two adjacent layers.
Each layer moves a distance dx in time dt relative to the layer below it. The ratio dx/dt must be the
change in velocity between layers so du = dx/dt.
When any material is deformed sideways by a (shear) force acting in the same direction, a shear stress τ
is produced between the layers and a corresponding shear strain γ is produced. Shear strain is defined as
follows.
dy
dx
height of the layer being deformed
sideways deformation
γ = =
The rate of shear strain is defined as follows.
dy
du
dt dy
dx
time taken dt
shear strain = = γ γ& = =
It is found that fluids such as water, oil and air, behave in such a manner that the shear stress between
layers is directly proportional to the rate of shear strain.
τ = constant x γ&
Fluids that obey this law are called NEWTONIAN FLUIDS.
© D.J.DUNN
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Explanation:
