### Theory of Flight

The density of the immersed object relative to the density of the The buoyant force is then the difference between the forces at the top and bottom The atmosphere's density depends upon altitude. In such a case we calculate the average density. There is another term called specific gravity which is the ratio of the density of a material to the. of the submerged body. (volume of the submerged part of the body) Defn: Upthrust is equal to the weight of the fluid displaced. say Upthrust=F F= (density.. . 10, Views · How does the density of the air vary with altitude? 2, Views .

In this context, displacement is the term used for the weight of the displaced fluid and, thus, is an equivalent term to buoyancy. An object whose weight exceeds its buoyancy tends to sink. If the fluid density is greater than the average density of the object, the object floats; if less, the object sinks. Compressive fluids The atmosphere's density depends upon altitude.

As an airship rises in the atmosphere, its buoyancy reduces as the density of the surrounding air reduces. The density of water is essentially constant: Compressible objects As a floating object rises or falls the forces external to it change and, as all objects are compressible to some extent or another, so does the object's volume. Buoyancy depends on volume and so an object's buoyancy reduces if it is compressed and increases if it expands.

## Density, Pressure and Upthrust

If an object at equilibrium has a compressibility less than that of the surrounding fluid, the object's equilibrium is stable and it remains at rest. If, however, its compressibility is greater, its equilibrium is then unstableand it rises and expands on the slightest upward perturbation, or falls and compresses on the slightest downward perturbation. Submarines rise and dive by filling large tanks with seawater. To dive, the tanks are opened to allow air to exhaust out the top of the tanks, while the water flows in from the bottom.

### schoolphysics ::Welcome::

Once the weight has been balanced so the overall density of the submarine is equal to the water around it, it has neutral buoyancy and will remain at that depth. Normally, precautions are taken to ensure that no air has been left in the tanks. If air were left in the tanks and the submarine were to descend even slightly, the increased pressure of the water would compress the remaining air in the tanks, reducing its volume.

Since buoyancy is a function of volume, this would cause a decrease in buoyancy, and the submarine would continue to descend. The height of a balloon tends to be stable. This is the only way he can maintain an approximately constant altitude, since maintaining a strictly constant altitude by way of maintaining a net zero buoyant force on the balloon is practically impossible. If the balloon operator wishes to move the balloon sideways in a horizontal direction he must know, ahead of time, the wind direction, which varies with altitude.

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So he simply raises or lowers the hot air balloon to the altitude corresponding to the wind direction he wants, which is the direction he wants the balloon to go.

The balloon stays inflated because the heated air inside the envelope creates a pressure greater than the surrounding air.

However, since the envelope has an opening at the bottom above the location of the burnerthe expanding hot air is allowed to escape, preventing a large pressure differential from developing. This means that the pressure of the heated air inside the balloon ends up being only slightly greater than the cooler surrounding air pressure.

An efficient hot air balloon is one that minimizes the weight of the balloon components, such as the envelope, and on board equipment such as the burner and propane fuel tanks. This in turn minimizes the required temperature of the air inside the envelope needed to generate sufficient buoyant force to generate lift. Minimizing the required air temperature means that you minimize the burner energy needed, thereby reducing fuel use. Hot Air Balloon Physics — Analysis Let's examine the physics of a hot air balloon using a sample calculation.

The heated air inside the envelope is at roughly the same pressure as the outside air.

### Hot Air Balloon Physics

With this in mind we can calculate the density of the heated air at a given temperature, using the Ideal gas law, as follows: This is the density of the heated air inside the envelope. Compare this to normal ambient air density which is approximately 1.

Next, for an average size balloon with an envelope volume of m3 we wish to determine the net upward buoyant force generated by the envelope. The net buoyant force is defined here as the difference in density between the surrounding air and the heated air, multiplied by the envelope volume.

Air's density is very small compared to most solids and liquids. For this reason, the weight of an object in air is approximately the same as its true weight in a vacuum.

The buoyancy of air is neglected for most objects during a measurement in air because the error is usually insignificant typically less than 0. Pressure distribution on an immersed cube Forces on an immersed cube Approximation of an arbitrary volume as a group of cubes A simplified explanation for the integration of the pressure over the contact area may be stated as follows: Consider a cube immersed in a fluid with the upper surface horizontal.

The sides are identical in area, and have the same depth distribution, therefore they also have the same pressure distribution, and consequently the same total force resulting from hydrostatic pressure, exerted perpendicular to the plane of the surface of each side. There are two pairs of opposing sides, therefore the resultant horizontal forces balance in both orthogonal directions, and the resultant force is zero.

The upward force on the cube is the pressure on the bottom surface integrated over its area. The surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of the horizontal bottom surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the bottom surface.

Similarly, the downward force on the cube is the pressure on the top surface integrated over its area.

Therefore, the integral of the pressure over the area of the horizontal top surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the top surface. As this is a cube, the top and bottom surfaces are identical in shape and area, and the pressure difference between the top and bottom of the cube is directly proportional to the depth difference, and the resultant force difference is exactly equal to the weight of the fluid that would occupy the volume of the cube in its absence.

This means that the resultant upward force on the cube is equal to the weight of the fluid that would fit into the volume of the cube, and the downward force on the cube is its weight, in the absence of external forces. This analogy is valid for variations in the size of the cube. If two cubes are placed alongside each other with a face of each in contact, the pressures and resultant forces on the sides or parts thereof in contact are balanced and may be disregarded, as the contact surfaces are equal in shape, size and pressure distribution, therefore the buoyancy of two cubes in contact is the sum of the buoyancies of each cube.

This analogy can be extended to an arbitrary number of cubes. An object of any shape can be approximated as a group of cubes in contact with each other, and as the size of the cube is decreased, the precision of the approximation increases. The limiting case for infinitely small cubes is the exact equivalence. Angled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components and each dealt with in the same way.