Viscosity
The viscous force acting between two adjacent layers of a
liquid is directly proportional to the
surface area of the layers in contact and the velocity gradient. The viscous
force acts tangential to the liquid and in opposite direction to the direction
of flow of liquid. Hence negative sign
is used. It is like a frictional force acting against the relative motion.
It can be defined as
the tangential force per unit area required to maintain unit velocity gradient.
(or) It is the ratio between tangential stress and velocity gradient.
Effect of temperature on Viscosity
In the case of liquids, coefficient of viscosity decreases with
increase of temperature as the cohesive forces decrease with increase of
temperature.In the case of gases,coefficient of viscosity increases with
increase of temperature because the change in momentum of molecules increases
with increase of temperature.
In the case of liquids with increase in temperature, distance
between molecules increases . This leads to
the decrease of force of attraction .
In the case of gases, with the increase in temperature,
random motion of molecules increases and collisions also increases. This
increases viscous nature.
Effect of pressure
In a liquids the value of increases with increase of
pressure. For gases, its value of
increases with increase of pressure at low pressure. But at high pressure, it is independent of pressure.
Raynold’s Number
We can decide the flow of the fluid as is a streamlined flow
or not basing on a value called Raynold’s number.
The velocity at which the streamlined flow turns into a
non-streamline flow is called as critical velocity. Critical velocity of a
fluid is directly proportional to coefficient of viscosity, inversely
proportional to diameter of the fluid flow and also inversely proportional to
the density of the fluid. We can write the equation by keeping all of these
things together. The proportionality can be eliminated with a constant as shown
below.
Terminal velocity
A constant velocity is acquired by a body when the resultant
force acting on it is zero and it is called as terminal velocity. When a
spherical body is moving in a fluid its weight always acts in downward
direction and it’s upthrust always acts in upward direction. The medium applies a force against its motion and it is called viscous force. The direction of
the viscous forces always against the relative motion of the body in the fluid.
When the body is initially in the state of rest there is no
viscous force acting on it. When the body starts coming down it’s velocity
increases due to the gravitational force and automatically viscous force also
starts increasing against the
gravitational force.
At a certain stage the downward force is balanced by the up ward
force therefore the body will acquire a constant velocity and that velocity is
called as terminal velocity. By drawing the condition for equilibrium we can
derive the equation further terminal velocity as shown below.
Special Case
When multiple drops are falling with a different terminal
velocities and if the drops are combined together to form a big drop we can
derive a equation further terminal velocity of the big drop as shown below.
While solving this problem we are going to depend on the
simple concept that volume of the big drop is equal to the sum of the volume of
all the small drops together. We can also express the terminal velocity in
terms of the mass is shown in the below diagram.
Poisellie’s Equation
This equation helps in identifying the volume of the fluid
flowing through a given hole per second.It depends on radius of tube with power four,pressure and inversely proportional to its length and coefficient of viscosity.Keeping only pressure in the numerator, every thing can be shifted to denominator and hence it oppose the flow of fluid.Then it is being called as fluid resistance.
When the pipes are connected in series, the same volume of the fluid flows through them and pressure at different points is going to be different.
When the pipes are connected in parallel, volume of fluid will be shared across them but pressure across two pipes is going to be the same.
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