When you draw water up through a pipe (or straw) by removing the air inside that pipe, you are allowing the atmospheric pressure around the water to push the water up the pipe. The water experiences a pressure imbalance between the pressure around it (atmospheric pressure) and the pressure in the pipe (less than atmospheric pressure), so it accelerates into the pipe. But as the water column inside the pipe grows taller, a new problem appears: gravity. The water's weight pushes downward and begins to oppose the pressure imbalance. At a certain height, the two effects balance and the water stops accelerating upward. When the water's height reaches 10 m, atmospheric pressure can't overcome this weight problem, even if all the air has been removed from the pipe.
When you fill a straw with water and then seal one end with your finger, you can then hold the straw vertically without any water falling out of the straw. That's because the air pressure above the column of water decreases until the upward force caused by the unbalanced pressure at the top and bottom of the water column is exactly equal to the weight of the water column. The drop in pressure above the water column occurs because the water initial does fall downward. When you first tip the straw from horizontal to vertical, the air pressures above and below the water column are equal and there is no pressure force to opposite the weight of the water. The water begins to fall. As it does, it creates a relatively empty region above the water column and below your finger. The air molecules in that region become sparser and their pressure decreases as a result. The water descends just far enough to lower the pressure inside that trapped air region until the pressure force balances the water's weight. Actually, the water column bounces up and down briefly, just like a weight at the end of a spring or a person at the end of a bungee cord. But after a second or so, the water column just hangs there motionless in the straw, supported against gravity by the pressure imbalance. If air could work its way through the water column and enter the trapped region between the water column and your finger, the water column would be able to descend further. But the straw is so narrow and the water sticks to tightly to itself (a phenomenon called surface tension) that it prevents air bubbles from working their way up the straw.
First, I should point out that high pressure air/fluids can move either fast or slow, depending on the situation. The same holds for low-pressure air/fluids. What Bernoulli's equation tells us is that when air/fluids slows down, its pressure rises (assuming that it isn't moving up or down so that gravity is out of the picture) and when air/fluids speed up, its pressure drops. Here are two common examples.
First, when you spray water from a garden hose against your hand, the water goes from moving quickly through the air at atmospheric pressure to moving slowly on your hand at more than atmospheric pressure. You know that this pressure increase has occurred because you feel the water pushing hard on your hand. The water is exchanging kinetic energy for pressure potential energy and its pressure is rising.
Second, when you put your thumb over the end of the garden hose and allow only a fine spray to emerge, the water goes from slow moving water at high pressure inside the hose to fast moving water at atmospheric pressure in the air. You know that this pressure drop has occurred because you feel the water in the hose pushing hard against your thumb. The water is exchanging pressure potential energy for kinetic energy and its pressure is dropping.
When the wind blows into your room, it comes to a stop and experiences a rise in pressure. This is an consequence of Bernoulli's equation, which recognizes that energy is conserved and that in a fluid, energy can exist either as kinetic energy (energy of motion), pressure energy, or gravitational potential energy. In this case, the wind's kinetic energy becomes pressure energy as it slow down in your room. As the pressure in your room rises, it prevents more air from entering, so you have high pressure but no movement inside your room. As soon as you open the door, the high-pressure air in your room accelerates toward the relatively low-pressure air in your hall. The pressure in your room drops and the wind can get in now. Soon the wind is blowing right through your room, as though you were part of a wind tunnel. If the wind is cold, you will be too.
When a fluid is flowing smoothly and steadily through a stationary environment, its energy is conserved. As long as it doesn't lose much energy to frictional effects, you can count on its total energy remaining essentially constant as it flows downstream. Since it only has three forms for its energy: gravitational potential energy, pressure potential energy, and kinetic energy, you can expect that a decrease in one of these forms of energy will be accompanied by an increase in one of the other forms. That's when speed and pressure are inversely related. When the fluid slows down, its kinetic energy drops so its pressure potential energy (and its pressure) must rise.
There are many different types of flow meters, some specialized to handling gases and others to handling liquids. In each case, a true flow meter transfers gas from its inlet to its outlet one unit of volume at a time and it measures how many of those volumes it transfers. There are also some flow rate meters that measure how quickly a gas or liquid is flowing. These devices normally use of turbines to measure the speed of the passing fluid and measurements from these flow rate meters can be integrated over time to determine how much gas or liquid has passed through them. However, because flow rate meters don't measure each volume of gas directly, they aren't as accurate as true flow meters.
Let me assume that you want to know about a turbine flow meter for gas. The most common of these is a device that's half filled with liquid. The "turbine" is actually a set of blades that spin in a vertical plane and spend half their times immersed in the liquid. When one of the turning blades emerges from the liquid, the empty space that appears beneath it is allowed to fill with the gas being measured. This gas flows in from the meter's inlet. Soon another blade begins to emerge from the liquid and a volume of gas is then trapped between the first blade and the second blade. Once the blades have turned almost half a turn, the first one begins to submerge again in the liquid. The gas that was trapped between it and the next blade is then squeezed out from between those blades by the liquid and flows out the meter's outlet. A geared arrangement measures how many turns the blades make and therefore how many volumes of gas have been transferred from the meter's inlet to its outlet.
A Bourdon tube pressure gauge works on much the same principle as a party favor that inflates and unrolls when you blow in its tube. The hollow Bourdon tube of the pressure gauge isn't circular in cross-section—it's somewhat oval. When the pressure inside the tube increases, the tube's oval walls are distorted and the tube's cross-section becomes slightly more circular. However, the tube is wrapped in a coil and as its walls become more circular, the tube uncoils slightly. The amount of uncoiling that occurs is almost exactly proportional to the pressure inside the Bourdon tube. As the tube uncoils, its motion activates a rack-and-pinion gear system that turns the needle on the pressure dial of the gauge. While all that you see when you look at the gauge is this needle pointing at the current pressure, you should understand that there is a small, bent tube that's coiling and uncoiling with each change in the pressure inside that tube.
I believe that the pump you're interested in is one that uses the energy released when water flows downhill to lift a small fraction of that water upward. While there are many possible designs for such a pump, the classic version used a phenomenon called "water hammer" to lift water upward. In this technique, a column of water is allowed to accelerate downhill through a pipe until it's flowing at a good speed through the pipe. The pump then closes a valve at the lower end of the pipe, so that the water has to stop abruptly. Since water accelerates in response to imbalances in pressure, the stopping process involves an enormous pressure surge at the lower end of the moving water column. A one-way valve at the lower end of the pipe opens during this pressure surge and allows a small fraction of the water to escape from the pipe. The escaping water rises upward through a second pipe for delivery to a home or business. According to a reader, the escaping water actually enters a head tank that is normally filled with air and thus compresses that air. The compressed air is then used to push water through the pump's outlet and provide the pumping action. This pumping scheme is apparently called a "hydraulic ram."
The only trick to operating such a pump is opening and closing the valve at the lower end of the first pipe. This valve must open long enough that the water in the pipe reaches a good speed and then it must close very suddenly to provide the pressure surge that lifts the small amount of water upward for delivery.
A typical bicycle pump uses a piston to squeeze air that it has trapped inside a cylinder. As you push the piston into the cylinder, the trapped air molecules are packed more tightly together and their pressure rises. Moreover, because you are transferring energy to the air by doing mechanical work on it, the air's temperature also rises. Air always accelerates toward regions of lower pressure, so this pressurized air will tend to flow through any opening that leads to lower pressure—such as the inside of an underinflated bicycle tire. A one-way valve at the base of the cylinder allows this pressurized air to flow out of the cylinder through a pipe and enter the bicycle tire. Thus each time you push down on the piston, you pressurize the air inside the cylinder and it accelerates and flows toward the lower pressure inside the bicycle tire. As you pull the piston out of the cylinder, a second one-way valve allows new air to enter the cylinder from outside so that you can repeat this process.
In a pumped air athletic shoe, squeezing a rubber bulb packs together air molecules and increases their pressure. When the pressure is high enough, a one-way valve allows this pressurized air to flow into the underinflated air pocket of the shoe. A second one-way valve allows the bulb to refill with outside air when you stop squeezing the bulb. Once the air pocket has been filled with large numbers of air molecules, these molecules exert substantial outward forces on the inner surfaces of that air pocket. The more molecules there are inside the pocket, the more often they collide with the surfaces and the more force they exert on those surfaces. These outward forces from the air molecules allow the air pocket keeps its shape.
If the speed of the water were uniform as it passes through the opening, you could measure that speed and multiply it by the cross-section of the weir to obtain the volume of water passing through the weir each second. However, since the flow is faster near the center of the flow, it's difficult to calculate the volume flowing each second. Your best bet is probably to divide the opening into a number of regions and then to measure the water's velocity at the center of each region. Multiply each velocity by the cross-sectional area of that region and then sum up all the products to obtain the overall volume flow per second.
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