viscosity




Viscosity is internal friction in a fluid. Viscous forces oppose the motion of one portion of a fluid relative to another. Viscosity is the reason it takes effort to paddle a canoe through calm water, but it is also the reason the paddle works. Viscous effects are important in the flow of fluids in pipes, the flow of blood, the lubrication of engine parts, and many other situations

Fluids that flow readily, such as water or gasoline, have smaller viscosities than do “thick” liquids such as honey or motor oil. Viscosities of all fluids are strongly temperature dependent, increasing for gases and decreasing for liquids as the temperature increases (Fig. 12.28). Oils for engine lubrication must flow equally well in cold and warm conditions, and so are designed to have as little temperature variation of viscosity as possible.

viscosity

 

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A viscous fluid always tends to cling to a solid surface in contact with it. There is always a thin boundary layer of fluid near the surface, in which the fluid is nearly at rest with respect to the surface. That’s why dust particles can cling to a fan blade even when it is rotating rapidly, and why you can’t get all the dirt off your car by just squirting a hose at it.

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Viscosity has important effects on the flow of liquids through pipes, including the flow of blood in the circulatory system. First think about a fluid with zero viscosity so that we can apply Bernoulli’s equation, Eq. (12.17). If the two ends of a long cylindrical pipe are at the same height (y1 = y2) and the flow speed is the same at both ends (v1 = v2), Bernoulli’s equation tells us that the pressure

 


is the same at both ends of the pipe. But this isn’t true if we account for viscosity.
To see why, consider Fig. 12.29, which shows the flow-speed profile for laminar
flow of a viscous fluid in a long cylindrical pipe. Due to viscosity, the speed is zero
at the pipe walls (to which the fluid clings) and is greatest at the center of the pipe.
The motion is like a lot of concentric tubes sliding relative to one another, with the
central tube moving fastest and the outermost tube at rest. Viscous forces between
the tubes oppose this sliding, so to keep the flow going we must apply a greater pressure
at the back of the flow than at the front. That’s why you have to keep squeezing
a tube of toothpaste or a packet of ketchup (both viscous fluids) to keep the fluid
coming out of its container. Your fingers provide a pressure at the back of the
flow that is far greater than the atmospheric pressure at the front of the flow.

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viscosity

 

 

 

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The pressure difference required to sustain a given volume flow rate through
a cylindrical pipe of length L and radius R turns out to be proportional to L/R4
.
If we decrease R by one-half, the required pressure increases by 24 = 16;
decreasing R by a factor of 0.90 (a 10% reduction) increases the required pressure
difference by a factor of (1/0.90)4 = 1.52 (a 52% increase). This simple
relationship explains the connection between a high-cholesterol diet (which tends
to narrow the arteries) and high blood pressure. Due to the R4
 dependence, even a
small narrowing of the arteries can result in substantially elevated blood pressure
and added strain on the heart muscle

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Uncertainty And Significant Figures Viscosity
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Fluid Mechanics The Motion Of Satellites

 

 



Frequently Asked Questions

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Ans: HERE ARE SOME EXAMPLES TO DEAL WITH view more..
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Ans: To derive Bernoulli’s equation, we apply the work–energy theorem to the fluid in a section of a flow tube. In Fig. 12.23 we consider the element of fluid that at some initial time lies between the two cross sections a and c. The speeds at the lower and upper ends are v1 and v2. In a small time interval dt, the fluid that is initially at a moves to b, a distance ds1 = v1 dt, and the fluid that is initially at c moves to d, a distance ds2 = v2 dt. The cross-sectional areas at the two ends are A1 and A2, as shown. The fluid is incompressible; hence by the continuity equation, Eq. (12.10), the volume of fluid dV passing any cross section during time dt is the same. That is, dV = A1 ds1 = A2 ds2. view more..
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Ans: According to the continuity equation, the speed of fluid flow can vary along the paths of the fluid. The pressure can also vary; it depends on height as in the static situation (see Section 12.2), and it also depends on the speed of flow. We can derive an important relationship called Bernoulli’s equation, view more..
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Ans: Viscosity is internal friction in a fluid. Viscous forces oppose the motion of one portion of a fluid relative to another. Viscosity is the reason it takes effort to paddle a canoe through calm water, but it is also the reason the paddle works. Viscous effects are important in the flow of fluids in pipes, the flow of blood, the lubrication of engine parts, and many other situations view more..
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Ans: When the speed of a flowing fluid exceeds a certain critical value, the flow is no longer laminar. Instead, the flow pattern becomes extremely irregular and complex, and it changes continuously with time; there is no steady-state pattern. This irregular, chaotic flow is called turbulence view more..
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Ans: SUMMARY OF EVERY TOPIC OF FLUID MECHANISM. view more..
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Ans: Some of the earliest investigations in physical science started with questions that people asked about the night sky. Why doesn’t the moon fall to earth? Why do the planets move across the sky? Why doesn’t the earth fly off into space rather than remaining in orbit around the sun? The study of gravitation provides the answers to these and many related questions view more..
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Ans: Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. view more..
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Ans: We have stated the law of gravitation in terms of the interaction between two particles. It turns out that the gravitational interaction of any two bodies having spherically symmetric mass distributions view more..
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Ans: To determine the value of the gravitational constant G, we have to measure the gravitational force between two bodies of known masses m1 and m2 at a known distance r. The force is extremely small for bodies that are small enough to be brought into the laboratory, but it can be measured with an instrument called a torsion balance, which Sir Henry Cavendish used in 1798 to determine G. view more..
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Ans: HERE ARE SOME SOLVED EXAMPLES TO CLEAR YOUR CONCEPTS view more..
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Ans: gravitational forces are negligible between ordinary household-sized objects but very substantial between objects that are the size of stars. Indeed, gravitation is the most important force on the scale of planets, stars, and galaxies view more..
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Ans: We defined the weight of a body in Section 4.4 as the attractive gravitational force exerted on it by the earth. We can now broaden our definition and say that the weight of a body is the total gravitational force exerted on the body by all other bodies in the universe view more..
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Ans: When we first introduced gravitational potential energy in Section 7.1, we assumed that the earth’s gravitational force on a body of mass m doesn’t depend on the body’s height. This led to the expression U = mgy view more..
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Ans: As a final note, let’s show that when we are close to the earth’s surface, Eq. (13.9) reduces to the familiar U = mgy view more..
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Ans: Artificial satellites orbiting the earth are a familiar part of technology But how do they stay in orbit, and what determines the properties of their orbits? We can use Newton’s laws and the law of gravitation to provide the answers. In the next section we’ll analyze the motion of planets in the same way. view more..
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Ans: A circular orbit, like trajectory 4 in Fig. 13.14, is the simplest case. It is also an important case, since many artificial satellites have nearly circular orbits and the orbits of the planets around the sun are also fairly circular view more..
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Ans: The name planet comes from a Greek word meaning “wanderer,” and indeed the planets continuously change their positions in the sky relative to the background of stars. One of the great intellectual accomplishments of the 16th and 17th centuries was the threefold realization that the earth is also a planet, that all planets orbit the sun, and that the apparent motions of the planets as seen from the earth can be used to determine their orbits precisely view more..




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