Although this force seems large, it is small compared with the [latex] 1. In fact, it is only 0. If the reservoir in Figure covered twice the area, but was kept to the same depth, would the dam need to be redesigned? The pressure found in part a of the example is completely independent of the width and length of the lake; it depends only on its average depth at the dam. In the diagram, note that the thickness of the dam increases with depth to balance the increasing force due to the increasing pressure.
A static fluid is a fluid that is not in motion. At any point within a static fluid, the pressure on all sides must be equal—otherwise, the fluid at that point would react to a net force and accelerate. The pressure at any point in a static fluid depends only on the depth at that point. As discussed, pressure in a fluid near Earth varies with depth due to the weight of fluid above a particular level. In the above examples, we assumed density to be constant and the average density of the fluid to be a good representation of the density.
This is a reasonable approximation for liquids like water, where large forces are required to compress the liquid or change the volume. In a swimming pool, for example, the density is approximately constant, and the water at the bottom is compressed very little by the weight of the water on top. Traveling up in the atmosphere is quite a different situation, however. Fluid located at deeper levels is subjected to more force than fluid nearer to the surface due to the weight of the fluid above it.
Therefore, the pressure calculated at a given depth is different than the pressure calculated using a constant density. Imagine a thin element of fluid at a depth h , as shown in Figure. The weight of the element itself is also shown in the free-body diagram. The weight of the element itself is shown in the free-body diagram.
Using a Cartesian y -axis oriented up, we find the following equation for the y -component:. Note that if the element had a non-zero y -component of acceleration, the right-hand side would not be zero but would instead be the mass times the y -acceleration. The mass of the element can be written in terms of the density of the fluid and the volume of the elements:. This equation tells us that the rate of change of pressure in a fluid is proportional to the density of the fluid.
If the range of the depth being analyzed is not too great, we can assume the density to be constant. But if the range of depth is large enough for the density to vary appreciably, such as in the case of the atmosphere, there is significant change in density with depth.
In that case, we cannot use the approximation of a constant density. Note that the pressure in a fluid depends only on the depth from the surface and not on the shape of the container. Thus, in a container where a fluid can freely move in various parts, the liquid stays at the same level in every part, regardless of the shape, as shown in Figure. In the container pictured, the pressure at the bottom of each column is the same; if it were not the same, the fluid would flow until the pressures became equal.
The change in atmospheric pressure with height is of particular interest. Assuming the temperature of air to be constant, and that the ideal gas law of thermodynamics describes the atmosphere to a good approximation, we can find the variation of atmospheric pressure with height, when the temperature is constant.
We discuss the ideal gas law in a later chapter, but we assume you have some familiarity with it from high school and chemistry. Let p y be the atmospheric pressure at height y. Thus, atmospheric pressure drops exponentially with height, since the y -axis is pointed up from the ground and y has positive values in the atmosphere above sea level. This gives us only a rough estimate of the actual situation, since we have assumed both a constant temperature and a constant g over such great distances from Earth, neither of which is correct in reality.
Fluid pressure has no direction, being a scalar quantity, whereas the forces due to pressure have well-defined directions: They are always exerted perpendicular to any surface. The reason is that fluids cannot withstand or exert shearing forces.
Thus, in a static fluid enclosed in a tank, the force exerted on the walls of the tank is exerted perpendicular to the inside surface. Likewise, pressure is exerted perpendicular to the surfaces of any object within the fluid. Figure illustrates the pressure exerted by air on the walls of a tire and by water on the body of a swimmer.
The arrows represent directions and magnitudes of the forces exerted at various points. The arrows represent the directions and magnitudes of the forces exerted at various points on the swimmer. Note that the forces are larger underneath, due to greater depth, giving a net upward or buoyant force. The net vertical force on the swimmer is equal to the sum of the buoyant force and the weight of the swimmer.
Which of the following substances are fluids at room temperature and atmospheric pressure: air, mercury, water, glass? Mercury and water are liquid at room temperature and atmospheric pressure. Air is a gas at room temperature and atmospheric pressure. Glass is an amorphous solid non-crystalline material at room temperature and atmospheric pressure. At one time, it was thought that glass flowed, but flowed very slowly. This theory came from the observation that old glass planes were thicker at the bottom.
It is now thought unlikely that this theory is accurate. The density of air decreases with altitude. For a column of air of a constant temperature, the density decreases exponentially with altitude. This is a fair approximation, but since the temperature does change with altitude, it is only an approximation.
The image shows a glass of ice water filled to the brim. Will the water overflow when the ice melts? Explain your answer. How is pressure related to the sharpness of a knife and its ability to cut? Pressure is force divided by area. If a knife is sharp, the force applied to the cutting surface is divided over a smaller area than the same force applied with a dull knife.
The concept of mass flow in terms of throughput is even more important when gas loads during process are considered. Thermally induced desorption from a radiating evaporation source would be a good example. If the new pressure does not rise to an area where the pumping speed is lower, the pump will be able to handle the gas load and maintain a fixed and expected new pressure. In some cases, the pump will not be able to handle the increase at all. An ion pump with a gas load that raises the pressure above 10 -5 torr would be a good example, since the steadily lowering pumping speed and throughput would cause the pump to overheat and shut down.
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Mass is a measure of the amount of material in an object, directly related to the number and type of atoms present in the object. Mass does not change with a body's position, movement or alteration of its shape unless material is added or removed. The unit of mass in the SI system is the kilogram kg. In the trading of goods, weight is taken to mean the same as mass and is measured in kilograms.
Scientifically, however, it is normal to state that the weight of a body is the gravitational force acting on it and hence it should be measured in newtons N , and that this force depends on the local force due to gravity. Sometimes people ask "If light has no mass how can it be deflected by the gravity of a star? One answer is that all particles, including photons, move along geodesics in general relativity and the path they follow is independent of their mass.
The deflection of starlight by the sun was first measured by Arthur Eddington in The result was consistent with the predictions of general relativity and inconsistent with the newtonian theory. Another answer is that the light has energy and momentum which couples to gravity. The energy-momentum 4-vector of a particle, rather than its mass, is the gravitational analogue of electric charge. The corresponding analogue of electric current is the energy-momentum stress tensor which appears in the gravitational field equations of general relativity.
The energy and momentum of light also generates curvature of spacetime, so general relativity predicts that light will attract objects gravitationally. This effect is far too weak to have yet been measured.
The gravitational effect of photons does not have any cosmological effects either except perhaps in the first instant after the Big Bang. And there seem to be far too few with too little energy to make any noticeable contribution to dark matter. For an alternative viewpoint of relativistic mass, see the article by T.
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