# 12.4 Viscosity and laminar flow; poiseuille’s law  (Page 2/12)

 Page 2 / 12

[link] shows how viscosity is measured for a fluid. Two parallel plates have the specific fluid between them. The bottom plate is held fixed, while the top plate is moved to the right, dragging fluid with it. The layer (or lamina) of fluid in contact with either plate does not move relative to the plate, and so the top layer moves at $v$ while the bottom layer remains at rest. Each successive layer from the top down exerts a force on the one below it, trying to drag it along, producing a continuous variation in speed from $v$ to 0 as shown. Care is taken to insure that the flow is laminar; that is, the layers do not mix. The motion in [link] is like a continuous shearing motion. Fluids have zero shear strength, but the rate at which they are sheared is related to the same geometrical factors $A$ and $L$ as is shear deformation for solids.

A force $F$ is required to keep the top plate in [link] moving at a constant velocity $v$ , and experiments have shown that this force depends on four factors. First, $F$ is directly proportional to $v$ (until the speed is so high that turbulence occurs—then a much larger force is needed, and it has a more complicated dependence on $v$ ). Second, $F$ is proportional to the area $A$ of the plate. This relationship seems reasonable, since $A$ is directly proportional to the amount of fluid being moved. Third, $F$ is inversely proportional to the distance between the plates $L$ . This relationship is also reasonable; $L$ is like a lever arm, and the greater the lever arm, the less force that is needed. Fourth, $F$ is directly proportional to the coefficient of viscosity , $\eta$ . The greater the viscosity, the greater the force required. These dependencies are combined into the equation

$F=\eta \frac{\text{vA}}{L}\text{,}$

which gives us a working definition of fluid viscosity     $\eta$ . Solving for $\eta$ gives

$\eta =\frac{\text{FL}}{\text{vA}}\text{,}$

which defines viscosity in terms of how it is measured. The SI unit of viscosity is $\text{N}\cdot \text{m/}\left[\left(\text{m/s}\right){\text{m}}^{2}\right]=\left({\text{N/m}}^{2}\right)\text{s or Pa}\cdot \text{s}$ . [link] lists the coefficients of viscosity for various fluids.

Viscosity varies from one fluid to another by several orders of magnitude. As you might expect, the viscosities of gases are much less than those of liquids, and these viscosities are often temperature dependent. The viscosity of blood can be reduced by aspirin consumption, allowing it to flow more easily around the body. (When used over the long term in low doses, aspirin can help prevent heart attacks, and reduce the risk of blood clotting.)

## Laminar flow confined to tubes—poiseuille’s law

What causes flow? The answer, not surprisingly, is pressure difference. In fact, there is a very simple relationship between horizontal flow and pressure. Flow rate $Q$ is in the direction from high to low pressure. The greater the pressure differential between two points, the greater the flow rate. This relationship can be stated as

$Q=\frac{{P}_{2}-{P}_{1}}{R}\text{,}$

where ${P}_{1}$ and ${P}_{2}$ are the pressures at two points, such as at either end of a tube, and $R$ is the resistance to flow. The resistance $R$ includes everything, except pressure, that affects flow rate. For example, $R$ is greater for a long tube than for a short one. The greater the viscosity of a fluid, the greater the value of $R$ . Turbulence greatly increases $R$ , whereas increasing the diameter of a tube decreases $R$ .

Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
what's electromagnetic induction
electromagnetic induction is a process in which conductor is put in a particular position and magnetic field keeps varying.
Lukman
wow great
Salaudeen
what is mutual induction?
je
mutual induction can be define as the current flowing in one coil that induces a voltage in an adjacent coil.
Johnson
how to undergo polarization
show that a particle moving under the influence of an attractive force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v²k² and distance uk²/√u-vk as origin
show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
No idea.... Are you even sure this question exist?
Mavis
I can't even understand the question
yes it was an assignment question "^"represent raise to power pls
Gabriel
Gabriel
An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg . Pendulum 2 has a bob with a mass of 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º .
no ideas
Augstine
if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
Modern cars are made of materials that make them collapsible upon collision. Explain using physics concept (Force and impulse), how these car designs help with the safety of passengers.
calculate the force due to surface tension required to support a column liquid in a capillary tube 5mm. If the capillary tube is dipped into a beaker of water
find the time required for a train Half a Kilometre long to cross a bridge almost kilometre long racing at 100km/h
method of polarization
Ajayi
What is atomic number?
The number of protons in the nucleus of an atom
Deborah
type of thermodynamics
oxygen gas contained in a ccylinder of volume has a temp of 300k and pressure 2.5×10Nm
why the satellite does not drop to the earth explain
what is a matter
Yinka
what is matter
Yinka
what is matter
Yinka
what is a matter
Yinka
I want the nuclear physics conversation
Mohamed
because space is a vacuum and anything outside the earth 🌎 can not come back without an act of force applied to it to leave the vacuum and fall down to the earth with a maximum force length of 30kcm per second
Clara
at t=0second,aparticles moving in x-y plain with aconstant acceleration has avelocity of initial velocity =(3i-2j)m/s and is at the origion.at t=3second the particle's velocity is final velocity=(9i+7j)then how to find the acceleration?
how about the formula like v^2=u^2+2as
Bayuo
a=v-u/t
Doreen
what is physics
Yinka
why is there a maximum distance at which the image can exist behind a convex mirror
The ball of a simple pendulum take 0.255 to swing from its equilibrium position to one extreme. Calculate it period.
The Ball of a simple pendulum take 0.255 to swing from its equilibrium position to one extreme. calculate its period
Abubakr
why is there a maximum distance at which the image can exist behind a convex mirror
Alfred
amplitude=0 .255s period=4×.255=1.02 sec period is one complete cycle
MUKHTAR