## How do you calculate the change in water pressure as the diameter of the hose ch…

#### How do you calculate the change in water pressure as the diameter of the hose changes? – JH

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.

## How do you determine the volume of water passing through a weir? – R

#### How do you determine the volume of water passing through a weir? – R

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.

## How does an air pump work and how does the air pocket in a Nike Air or Reebok pu…

#### How does an air pump work and how does the air pocket in a Nike Air or Reebok pump shoe keep its form? — MD, Toronto, CA

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.

## How does a gravity powered water pump work?

#### How does a gravity powered water pump work? — JA, Hiawassee, GA

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.

## How does a Bourdon tube pressure gauge work? – AM

#### How does a Bourdon tube pressure gauge work? – AM

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.

## How does a turbine flow meter work?

#### How does a turbine flow meter work?

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.

## In the book section on Water Distribution, there was a question (exercise 5) abo…

#### In the book section on Water Distribution, there was a question (exercise 5) about a novelty straw. The answer says that the straw can’t be taller than 0.5 meters. I thought you could suck liquid up a straw 10 meters tall? Why can this straw only be 0.5 meters tall?

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.

## Is air a fluid or a gas or both?

#### Is air a fluid or a gas or both?

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).

## Please define the 3 types of energy that flowing water has?

#### Please define the 3 types of energy that flowing water has?

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.

## Water seeks areas of lowest pressure. Is this the concept behind low-pressure we…

#### Water seeks areas of lowest pressure. Is this the concept behind low-pressure weather systems bringing precipitation and high pressure bringing clear, dry conditions?

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.