# FLUID FLOW

We are now ready to consider motion of a fluid. Fluid flow can be extremely complex, as shown by the currents in river rapids or the swirling flames of a campfire. But we can represent some situations by relatively simple idealized models. An ideal fluid is a fluid that is incompressible (that is, its density cannot change) and has no internal friction (called viscosity). Liquids are approximately incompressible in most situations, and we may also treat a gas as incompressible if the pressure differences from one region to another are not too great. Internal friction in a fluid causes shear stresses when two adjacent layers of fluid move relative to each other, as when fluid flows inside a tube or around an obstacle. In some cases we can ignore these shear forces in comparison with forces arising from gravitation and pressure differences.

The path of an individual particle in a moving fluid is called a flow line. In steady flow, the overall flow pattern does not change with time, so every element passing through a given point follows the same flow line. In this case the “map” of the fluid velocities at various points in space remains constant, although the velocity of a particular particle may change in both magnitude and direction during its motion. A streamline is a curve whose tangent at any point is in the direction of the fluid velocity at that point. When the flow pattern changes with time, the streamlines do not coincide with the flow lines. We’ll consider only steady-flow situations, for which flow lines and streamlines are identical.

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The flow lines passing through the edge of an imaginary element of area, such as area A in Fig. 12.18, form a tube called a flow tube. From the definition of a flow line, in steady flow no fluid can cross the side walls of a given flow tube.

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Figure 12.19 shows the pattern of fluid flow from left to right around an obstacle. The photograph was made by injecting dye into water flowing between two closely spaced glass plates. This pattern is typical of laminar flow, in which adjacent layers of fluid slide smoothly past each other and the flow is steady. (A lamina is a thin sheet.) At sufficiently high flow rates, or when boundary surfaces cause abrupt changes in velocity, the flow can become irregular and chaotic.

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This is called turbulent flow (Fig. 12.20). In turbulent flow there is no steady-state pattern; the flow pattern changes continuously.

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Ans: We’ve seen that if an object is less dense than water, it will float partially submerged. But a paper clip can rest atop a water surface even though its density is several times that of water. This is an example of surface tension: view more..
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Ans: A body immersed in water seems to weigh less than when it is in air. When the body is less dense than the fluid, it floats. The human body usually floats in water, and a helium-filled balloon floats in air. These are examples of buoyancy, a phenomenon described by Archimedes’s principle: view more..
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Ans: The simplest pressure gauge is the open-tube manometer . The U-shaped tube contains a liquid of density r, often mercury or water. The left end of the tube is connected to the container where the pressure p is to be measured, and the right end is open to the atmosphere view more..
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Ans: We are now ready to consider motion of a fluid. Fluid flow can be extremely complex, as shown by the currents in river rapids or the swirling flames of a campfire. But we can represent some situations by relatively simple idealized models. An ideal fluid is a fluid that is incompressible (that is, its density cannot change) and has no internal friction (called viscosity). 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: 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: 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: 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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