scrollAmount=5 scrollDelay=5 class="style17" style="height: 21px" onclick=" FP_playSound(/*url*/'INFO.mp3')">यो नेपाली science students हरुकोलागी एउटा नयाँ प्रयोग हो । तपाइँले हामिलाइ सहयोग गर्न सक्नुहुने छ । त्यसकोलागी तपाइले टाइप गर्नुभएको drivations, formule र long and short question answer हामिलाइ पठाउन सक्नुहुन्छ । तपाइले पठाएको सामाग्रिसंग तपाँइको नाम समावेश गरिने छ । यसको अधिकार तपाइँमा निहित हुनेछ । त्यसको लागि तलको ठेगाना समाग्रिहरु पठाउनुहोस ।
Poiseulle derived the
relation for the volume of a liquid following per second through
a horizontal uniformly bored capillary tube maintained at
constant pressure difference at any cross-section. For this he
made following assumptions.
1.
Flow of the
liquid is streamlined that is layer of the liquids are parallel
to the axis of the capillary tube.
2.
Flow of the
liquid is steady and there is no acceleration of liquid layer at
any points.
3.
There is no
radial flow; it means there is constant pressure difference at
any cross-sections.
4.
The velocity
of the layer of the liquid in contact with wall of the vessel is
zero.
Let us consider a uniform
capillary tube of length l and radius a. A liquid of viscosity
eta is flowing through it. Let us consider a layer of liquid of
radius r from the axis of the capillary tube. The liquid layer
over this layer flows with lower velocity. Hence it opposes the
velocity of layer we considered. By the Newton’s law of
viscosity this opposing force is given by,
F= coffin
of viscosity of the
liquid x surface area in contact X velocity gradient
Again
another force on the layer of consideration due to the pressure
difference is given by,
F=
pressure difference p X area of cross-section.
At
steady state, these two forces are equal, then
Integrating
this relation we get,
-----------
(1)
Here
c is the constant of the integration,
When
r=a, then v=0; so we can write,
Then,
Therefore
above equation (1) becomes,
This represents the equation
of the parabola which gives the velocity distribution in
streamlined flow with respect to the axis of flow of the
capillary tube. It is independent of the length of the tube. The
graph between velocity and the radius of the liquid layer
cylinder is shown in adjoining figure below.
The
lengths of the arrow are proportional to the velocities at their
respective positions.
Let
us consider a thin cylindrical shell of radii r and r+dr, then
Volume
of the liquid flowing per second through the shell,
