Buoyancy




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:

Archimedes’s principle:: When a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.

 

 

Topics You May Be Interested In
Center Of Gravity Pascal Law
Shear Stress And Strain Solved Problems
Elasticity And Plasticity Determining The Value Of G
Gases Liquid And Density The Gravitational Force Between Spherical Mass Distributions
Pressure, Depth, And Pascals Law A Point Mass Inside A Spherical Shell

To prove this principle, we consider an arbitrary element of fluid at rest. The dashed curve in Fig. 12.11a outlines such an element. The arrows labeled dFrepresent the forces exerted on the element’s surface by the surrounding fluid.

The entire fluid is in equilibrium, so the sum of all the y-components of force on this element of fluid is zero. Hence the sum of the y-components of the surface forces must be an upward force equal in magnitude to the weight mg of the fluid inside the surface. Also, the sum of the torques on the element of fluid must be zero, so the line of action of the resultant y-component of surface force must pass through the center of gravity of this element of fluid.

Buoyancy

 

Topics You May Be Interested In
Using And Converting Units Buoyancy
Vectors And Vector Addition Turbulence
Equilibrium And Elasticity A Point Mass Inside A Spherical Shell
Conditions For Equilibrium A Visit To A Black Hole
Gases Liquid And Density Period And Amplitude In Shm

 

 

 

 

Topics You May Be Interested In
Estimates And Order Of Magnitudes Buoyancy
Vectors And Vector Addition Kepler's Second Law
Finding And Using The Center Of Gravity Apparent Weight And The Earth’s Rotation
Stress, Strain, And Elastic Moduli A Visit To A Black Hole
Tensile And Compressive Stress And Strain Detecting Black Holes

 

 

 

Now we replace the fluid inside the surface with a solid body having exactly the same shape (Fig. 12.11b). The pressure at every point is the same as before. So the total upward force exerted on the body by the fluid is also the same, again equal in magnitude to the weight mg of the fluid displaced to make way for the body. We call this upward force the buoyant force on the solid body. The line of action of the buoyant force again passes through the center of gravity of the displaced fluid (which doesn’t necessarily coincide with the center of gravity of the body).

Topics You May Be Interested In
Nature Of Physics Examples On Gravition
Conditions For Equilibrium The Motion Of Satellites
Solving Rigid-body Equilibrium Problems Kepler's Third Law
Summary Of Equilibrium And Elasticity A Visit To A Black Hole
Pressure In A Fluid Summary

When a balloon floats in equilibrium in air, its weight (including the gas inside it) must be the same as the weight of the air displaced by the balloon. A fish’s flesh is denser than water, yet many fish can float while submerged. These fish have a gas-filled cavity within their bodies, which makes the fish’s average density the same as water’s. So the net weight of the fish is the same as the weight of the water it displaces. A body whose average density is less than that of a liquid can float partially submerged at the free upper surface of the liquid. A ship made of steel (which is much denser than water) can float because the ship is hollow, with air occupying much of its interior volume, so its average density is less than that of water. The greater the density of the liquid, the less of the body is submerged. When you swim in seawater (density 1030 kg/m3 ), your body floats higher than in freshwater (1000 kg/m3 )

Buoyancy

 

 

Topics You May Be Interested In
Solving Physics Problems Pascal Law
Center Of Gravity Absolute Pressure And Gauge Pressure
Stress, Strain, And Elastic Moduli The Continuity Equation
Summary Of Equilibrium And Elasticity Kepler's Laws (firsts, Second, Third Laws) And The Motion Of Planets
Pressure In A Fluid Amplitude, Period, Frequency, And Angular Frequency

 

 

 

 

Topics You May Be Interested In
Stress, Strain, And Elastic Moduli The Gravitational Force Between Spherical Mass Distributions
Gases Liquid And Density Periodic Motion
Bernoulli's Equation Describing Oscillation
Turbulence Amplitude, Period, Frequency, And Angular Frequency
Kepler's Laws (firsts, Second, Third Laws) And The Motion Of Planets Simple Harmonic Motion

 

 

 

 

Topics You May Be Interested In
Solving Physics Problems Gravitation And Spherically Symmetric Bodies
Uncertainty And Significant Figures The Motion Of Satellites
Shear Stress And Strain A Point Mass Inside A Spherical Shell
Pascal Law The Escape Speed From A Star
Deriving Bernoullis Equation Simple Harmonic Motion

 

A practical example of buoyancy is the hydrometer, used to measure the density of liquids (Fig. 12.12a). The calibrated float sinks into the fluid until the weight of the fluid it displaces is exactly equal to its own weight. The hydrometer floats higher in denser liquids than in less dense liquids, and a scale in the top stem permits direct density readings. Hydrometers like this are used in medical diagnosis to measure the density of urine (which depends on a patient’s level of hydration). Figure 12.12b shows a type of hydrometer used to measure the density of battery acid or antifreeze. The bottom of the large tube is immersed in the liquid; the bulb is squeezed to expel air and is then released, like a giant medicine dropper. The liquid rises into the outer tube, and the hydrometer floats in this liquid.

 

Buoyancy

Topics You May Be Interested In
Equilibrium And Elasticity Summary Of Fluid Mechanism
Finding And Using The Center Of Gravity Kepler's First Law
Pressure, Depth, And Pascals Law A Point Mass Inside A Spherical Shell
Pressure Gauges Detecting Black Holes
Buoyancy Circular Motion And The Equations Of Shm


Frequently Asked Questions

+
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..
+
Ans: If the pressure inside a car tire is equal to atmospheric pressure, the tire is flat. The pressure has to be greater than atmospheric to support the car, so the significant quantity is the difference between the inside and outside pressures. When we say that the pressure in a car tire is “32 pounds” (actually 32 lb>in.2 , equal to 220 kPa or 2.2 * 105 Pa), we mean that it is greater than atmospheric pressure (14.7 lb>in.2 or 1.01 * 105 Pa) by this amount. view more..
+
Ans: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. view more..
+
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..
+
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..
+
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..
+
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..
+
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..
+
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..
+
Ans: HERE ARE SOME EXAMPLES TO DEAL WITH view more..
+
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..
+
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..
+
Ans: SUMMARY OF EVERY TOPIC OF FLUID MECHANISM. view more..
+
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..
+
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..
+
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..
+
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..
+
Ans: HERE ARE SOME SOLVED EXAMPLES TO CLEAR YOUR CONCEPTS view more..




Rating - 3/5
525 views

Advertisements