# SOLVED PROBLEMS

**Frequently Asked Questions**

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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: The mass of a moving fluid doesn’t change as it flows. This leads to an important
relationship called the continuity equation view more..

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Ans: HERE ARE SOME EXAMPLES TO DEAL WITH 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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