While it's easy to push on water, it's hard to pull on water. When you drink soda through a straw, you may feel like you're pulling on the water, but you're not. What you are actually doing is removing some air from the space inside the straw and above the water, so that the air pressure in that space drops below atmospheric pressure. The water column near the bottom of the straw then experiences a pressure imbalance: the usual atmospheric pressure below it and less-than-atmospheric pressure above it. That imbalance provides a modest upward force on the water column and pushes it up into your mouth.

So far, so good. But if you make that straw longer, you'll need to suck harder. That's because as the column of water gets taller, it gets heavier. It needs a more severe pressure imbalance to push it upward and support it. By the time the straw and water column get to be about 40 feet tall, you'll need to suck every bit of air out from inside the straw because the pressure imbalance needed to support a 40-foot column of water is approximately one atmosphere of pressure. If the straw is taller than 40 feet, you're simply out of luck. Even if you remove all the air from within the straw, the atmospheric pressure of the water below the straw won't be able to push the water up the straw higher than about 40 feet.

To get the water to rise higher in the straw, you'll need to install a pump at the bottom. The pump increases the water pressure there to more than 1 atmosphere, so that there is a bigger pressure imbalance available and therefore the possibility of supporting a taller column of water.

OK, so returning to your question: once a well is more than about 40 feet deep, getting the water to the surface requires a pump at the bottom. That pump can boost the water pressure well above atmospheric and thereby push the water to the surface despite the great height and weight of the water column. Suction surface pumps are really only practical for water that's a few feet below the surface; after that, deep pressure pumps are a much better idea.

You can only go a few feet under water before you'll no longer be able to draw air into your lungs through that hose. It's a pressure problem. The water pressure outside your chest increases rapidly as you go deeper, but the air pressure inside the hose and your mouth barely changes at all. Pretty soon, you'll have so much more pressure outside your lungs than inside them that you won't be able to draw in any more air. Your muscles just won't be strong enough.

The water pressure increases quickly with depth because each layer of water must support the weight of all the water layers above it. Since water is dense, heavy stuff, the weight piles on quickly and it takes only 10 meters (34 feet) of descent to increase the water pressure from atmospheric to twice atmospheric. In contrast, the air in the hose is light, fluffy stuff, so its pressure increases rather slowly with depth. Even though each layer of air has to support the weight of all the layers of air above it, the rise in pressure is extremely gradual. It takes miles of atmosphere above the earth for the air pressure to build up to atmospheric pressure near the ground. The air pressure in your hose is therefore approximately unchanged by your descent into the water.

With the water pressure outside rising quickly as you go deeper and the air pressure in your mouth rising incredibly slowly as you go deeper, you quickly find it hard to breathe. Your muscles can push your chest outward against a modest pressure imbalance between outside and inside. But by the time you're a few feet below the surface, you just can't draw air into your lungs through that hose anymore. You need pressurized air, such as that provided by a scuba outfit or a deep-sea diver's compressor system.

Actually, faster moving fluids don't necessarily have lower pressure. For example, a bottle of compressed air in the back of a pickup truck is still high-pressure air, even though it's moving fast. The real issue here is that when fluid speeds up in passing through stationary obstacles, its pressure drops. For example, when air rushes into the open but stationary mouth of a vacuum cleaner, that air experiences not only a rise in speed, it also experiences a drop in pressure. Similarly, when water rushes out of the nozzle of a hose, its speed increases and its pressure drops. This is simply conservation of energy: as the fluid gains kinetic energy, it must lose pressure energy. However, if there are sources of energy around--fans, pumps, or moving surfaces--then these exchanges of pressure for speed may no longer be present. That's why I put in the qualifier of there being only stationary obstacles.

They measure the volume of liquid they deliver and shut off when they have dispensed enough soda to fill the cup. Accurate volumetric flowmeters, such as those used in the dispensers, typically have a sophisticated paddlewheel assembly inside that turns as the liquid goes through a channel. When the paddlewheel has gone around the right number of times, an electronic valve closes to stop the flow of liquid.

While it may seem that you are somehow attracting the water to your mouth when you suck, you are really just making it possible for air pressure to push the water up toward you. By removing much of the air from within the hose, you are lowering the air pressure in the hose. There is then a pressure imbalance at the bottom end of the hose: the pressure outside the hose is higher than the pressure inside it. It's this pressure imbalance that pushes water into the hose and upward toward your mouth.

But air pressure can't push the water upward forever. As the column of water in the hose rises, its weight increases. Atmospheric pressure can only lift the column of water so high before the upward force on the water is balanced by the water's downward weight. Even if you remove all of the air inside the hose, atmospheric pressure can only support a column of water about 30 feet tall inside the hose. If you're higher than that on your balcony, the water won't reach you no matter how hard you try. The only way to send the water higher is to put a pump at the bottom end of the hose. This pump can push upward harder than atmospheric pressure can and it can support a taller column of water. That's why deep home wells have submersible pumps at their bottoms--they must pump the water upward because it's impossible to suck it upward more than 30 feet from above.

The water pumps in most cars are centrifugal pumps. These pumps work by spinning water around in a circle inside a cylindrical pump housing. The pump makes the water spin by pushing it with an impeller. The blades of this impeller project outward from an axle like the arms of turnstile and, as the impeller spins, the water spins with it. As the water spins, the pressure near the outer edge of the pump housing becomes much higher than near the center of the impeller. There are many ways to understand this rise in pressure, and here are two:

First, you can view the water between the impeller blades as an object traveling in a circle. Objects don't naturally travel in a circle--they need an inward force to cause them to accelerate inward as they spin. Without such an inward force, an object will travel in a straight line and won't complete the circle. In a centrifugal pump, that inward force is provided by high-pressure water near the outer edge of the pump housing. The water at the edge of the pump pushes inward on the water between the impeller blades and makes it possible for that water to travel in a circle. The water pressure at the edge of the turning impeller rises until it's able to keep water circling with the impeller blades.

You can also view the water as an incompressible fluid, one that obeys Bernoulli's equation in the appropriate contexts. As water drifts outward between the impeller blades of the pump, it must move faster and faster because its circular path is getting larger and larger. The impeller blades do work on the water so it moves faster and faster. By the time the water has reached the outer edge of the impeller, it's moving quite fast. But when the water leaves the impeller and arrives at the outer edge of the cylindrical pump housing, it slows down. Here is where Bernoulli's equation figures in. As the water slows down and its kinetic energy decreases, that water's pressure potential energy increases (to conserve energy). Thus the slowing is accompanied by a pressure rise. That's why the water pressure at the outer edge of the pump housing is higher than the water pressure near the center of the impeller.

When water is actively flowing through the pump, arriving through a hole near the center of the impeller and leaving through a hole near the outer edge of the pump housing, the pressure rise between center and edge of the pump isn't as large. However, this pressure rise never completely disappears and it's what propels the water through the car's cooling system.

A toilet is actually a very clever device that makes use of a siphon to extract the water from its bowl. A siphon is an inverted U-shaped pipe that can transfers water from a higher reservoir to a lower reservoir by lifting that water upward from the higher reservoir and then lowering it into the lower reservoir. In fact, the water is simply seeking its level, just as it would if you connected the two reservoirs with a pipe at their bottoms. In that case, the water in the higher reservoir would flow out of it and into the lower reservoir, propelled by the higher water pressure at the bottom of the higher reservoir. In the case of a siphon, it's still the higher water pressure in the higher reservoir that causes the water to flow toward the lower reservoir, but in the siphon the water must temporarily flow above the water levels in either reservoir on its way to the lower reservoir. The water is able to rise upward a short distance with the help of air pressure, which provides the temporary push needed to lift the water up and over to the lower reservoir. At the top of the siphon, there is a partial vacuum--a region of space with a pressure that's less than atmospheric pressure. The same kind of partial vacuum exists in a drinking straw when you suck on it and is what allows atmospheric pressure to push the beverage up toward your mouth.

In the toilet, the bowl is the higher reservoir and the sewer is the lower reservoir. The pipe that connects the bowl to the sewer rises once it leaves your view and then descends toward the sewer. Normally, that rising portion of the pipe isn't filled water--water only fills enough of the pipe to prevent sewer gases from flowing out into the room. As a result of this incomplete filling, the siphon doesn't transfer any water. But when you flush the toilet, a deluge of water from a storage tank rapidly fills the bowl and floods the siphon tube. The siphon then begins to function. It transfers water from the higher reservoir (the toilet bowl) to the lower reservoir (the sewer) and it doesn't stop until the bowl is basically empty. At that point, the siphon stops working because air enters the U-shaped tube with a familiar sound and water again accumulates in the bowl. When the storage tank has refilled with water, the toilet is ready for action again.

Without more information about the air in your tube, it's not possible to determine its pressure. Bernoulli's equation is frequently misunderstood to say that high-speed air is low-pressure air and that low speed air is high-pressure air--two observations that aren't necessarily true. Just because air is moving rapidly doesn't mean that its pressure is low. For example, the air in an airplane cabin is moving quickly but its pressure is higher than that of the air outside the cabin. Similarly, if you were to throw a tank of compressed air across the room, its pressure would remain high despite its increase in speed.

What Bernoulli's equation really says is that air has three forms for its energy and that as long as that air flows smoothly and without significant friction through a system of stationary obstacles, the sum of those three energies can't change. The three energies are kinetic energy (the energy of motion), gravitational potential energy, and an energy associated with pressure that I call pressure potential energy. The obstacles must remain stationary so that they can't do work on the air and thus change its total energy. Since the sum of those three energies doesn't change as air flows through a stationary environment, its pressure typically falls whenever its speed rises and vice versa. If the air also changes altitude significantly, then gravitational potential energy must be included in these energy exchanges.

So the reason why I can't answer your question about air in a pipe is that I don't know what the air's total energy was before it flowed through the pipe. While I can calculate the air's kinetic energy from its speed and we can neglect gravitational potential energy because the air isn't changing altitudes much in the pipe, I need to know what the air's total energy is in order to determine its pressure potential energy and thus its pressure.

When water flows through a hose, it has three main forms for its energy: kinetic energy, gravitational potential energy, and an energy associated with its pressure--which I'll call pressure potential energy. Since energy is conserved, the water's energy can't change as it flows through the hose (we'll ignore frictional forces here, although they really are pretty important in a hose). Let's assume that the hose is horizontal, so that the water's gravitational potential energy can't change. When the water enters a narrowing in the hose, the water must speed up to avoid delaying the water behind it. This increase in speed is associated with an increase in kinetic energy. Since the water's energy can't change, the increase in kinetic energy must be accompanied by a decrease in pressure. If the water then enters a widening in the hose, it slows down, its kinetic energy drops, and its pressure rises to conserve energy! If the hose then rises upward, so that the water's gravitational potential energy rises, the water's pressure must drop to conserve energy. In general, one form of energy can become another but the sum of those three forms can't change.

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.

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.

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 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.

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.

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.

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.

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 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.

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.

The goal of the water tower is to store water high in the air, where it has lots of gravitational potential energy. This stored energy can be converted to pressure potential energy or kinetic energy for delivery to homes. Since height is everything, building a cylindrical water tower is inefficient. Most of the water is then near the ground. By making the tower wider near the top, it puts most of its water high up.

Yes. When a fluid that's in steady state flow (moving smoothly and continuously past stationary obstacles) loses kinetic energy, its potential energy goes up--either its pressure rises or it moves upward against gravity. That assumes that the kinetic energy isn't being lost to thermal energy because of some terrible friction problem.

Not really. Fluids do accelerate toward lower pressures, so a low-pressure weather system does attract surface winds (the air near the surface of the earth accelerates toward regions of lower pressure). But the precipitation issues are generally related to temperature changes. Hot air can hold more moisture than cold air, so if a low-pressure system attracts air and causes hot and cold airs to mix, the new air temperature and moisture may be incompatible. When that happens, the moisture emerges from the air as water droplets and it rains.

Whenever water (or any incompressible fluid) passes fixed obstacles in a laminar flow, its total energy is conserved (we're neglecting friction effects--viscous drag). That total energy consists of (1) the water's gravitational potential energy (how high up it is), (2) the water's pressure potential energy (how hard it pushes on surfaces), and (3) the water's kinetic energy (how fast it's moving). Since the water's total energy doesn't change, a change in one of these forms of energy necessitates a change in one or both of the other forms. For example, if water speeds up during its flow, the water's pressure or height or both must decrease.

Air is both a gas (a material composed of many independent particles that normally expands to fill its container) and a fluid (a material that can be reshaped easily to take on the shape of its container).

The question itself said that the straw was only 0.5 meters tall. In the answer I was intending to point out that you can have as much tubing as you like in that straw, because it's only 0.5 meters tall overall. I didn't intend to mean that straws taller than 0.5 meters but shorter than 10 meters wouldn't work. Just that a short straw will work no matter how much tubing it contains. Sorry for an imperfect answer in the book. I'll change it in future editions.

The water is propelled by a pressure imbalance. When the water level in one container is higher than that in the other container, the pressures at the two ends of the siphon aren't equal. There is more pressure on the high water side than on the low water side. As a result, the water accelerates toward the low water side and the water levels gradually become equal.

Yes, but the effect is not so extreme. As the water from the water company enters the narrower pipes in your house, it does have to speed up slightly and its pressure does drop slightly. But its pressure is still well above atmospheric pressure. However, the fact that the water must move faster through the narrower pipes in your house means that this water loses energy relatively quickly in your house. And the more water you draw through your house's plumbing, the larger the fraction of its energy it loses. That's why drawing a huge amount of water out of one faucet will diminish the flow through another faucet--increasing the flow by opening that first faucet wastes the energy of the water reaching the second faucet and it flows out more slowly.

If the straw is horizontal and the water wasn't moving to begin with, it won't move toward your mouth unless you suck. To make the water accelerate, it must experience net force and the two ways to achieve that net force are (1) to create a pressure imbalance on the water's ends and (2) to have the water's weight accelerate it. In a horizontal force with no pressure imbalance on it, there is no net force on the water and it doesn't accelerate.

Yes. However, you often don't notice this because as you lower a volume of air downward, you displace a similar volume of air upward. Thus you can't just raise or lower air to observe changes in its gravitational potential energy. You'd have less trouble if you compressed the air tightly together, perhaps turning it into a liquid, and then raised or lowered it. It's gravitational potential energy would then be much more noticeable.