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## Convert gram/hour [g/h] to decigram/second [dg/s]

1 gram/hour [g/h] = 0,00277777777777778 decigram/second [dg/s]

#### Logarithmic Units.

From the history, definitions, and classification of logarithmic units to interesting examples of their use in acoustics, telecommunications, photography, and other fields.

Overview

Measuring Mass Flow

Thermal Flow Meters

Differential Flow Meters

Rotameters

Coriolis Flow Meters

Ultrasonic Flow Meters

Conversion to Volumetric Flow Rate

Applications

In Aerodynamics

## Overview

To measure the amount of fluid that passes through a unit of area at a specified unit of time we can use different calculations for the amount of fluid, but in this article, we will consider mass. Mass flow rate is dependent on the velocity with which the fluid flows, the area through which it flows, the density of the fluid, and the volume that flows through this area in a given time. If we know the mass, we only need to know either the volume or the density but do not have to know both, because we can express either of these values using mass and the other known value.

## Measuring Mass Flow

There are different ways to measure mass flow rate, and there are different types of meters that perform these measurements. Below we discuss some of the common types.

A thermal flow meter. The top picture shows the condition where the liquid is stationary and the bottom picture shows a liquid flow, as indicated by the arrows. Orange temperature sensors A and B measure temperature before and after the heater element H. When there is no liquid flow, it is the same, but when the liquid flows, the temperature registered by sensor B is higher. The temperature from both sensors is compared to determine the mass flow rate — the greater the temperature difference the higher the mass flow rate.

### Thermal Flow Meters

Thermal flow meters use differences in temperature to measure mass flow rate. There are two different types of these meters. In both types, the flow of fluid passing a heated element cools it down. One type of thermal flow meter measures how much heat is needed to keep the temperature constant. Here, the higher the mass flow — the greater heat is required to maintain the temperature. The other type of flow meter measures the difference between the point of initial contact with the current of fluid, and the point further along the element. The greater the mass flow — the greater the temperature difference. Such meters can be used to measure mass flow rate of liquids and also gases. When gases or liquids cause corrosion, special materials such as alloys are used for the parts of the meter that are submerged in the liquid or gas.

An orifice plate meter. The orifice plate partially obstructs the flow of fluid and this results in the change in pressure. The plate is marked in black and denoted with the letter P. A and B are pressure meters, with the pressure on meter A higher than the pressure on meter B. |

A flow nozzle meter. The nozzle, which partially obstructs the flow of fluid and changes pressure, is marked in black and denoted with the letter N. A and B are pressure meters, with the pressure on meter A higher than the pressure on meter B. |

A venturi tube meter. This configuration of the pipe results in pressure reduction in the constricted area. A and B are pressure meters, with the pressure on meter A higher than the pressure on meter B. |

### Differential Flow Meters

These meters create a difference in pressure between two points, usually by obstructing the flow in some way. The difference in pressure is then measured, and the greater the mass flow rate — the greater this difference. For example **orifice plate meters** have a plate in the shape of a ring that restricts the amount of water that can pass through the area, where this plate is installed. **Flow nozzle meters** use a nozzle inside the pipe to narrow the diameter through which the fluid flows, and **Venturi tube meters** use a special tube that narrows and then returns back to the original diameter. You've probably seen a Venturi tube on a light aircraft where it is used to drive air-driven gyroscopic instruments. The pipe in Venturi tube meters is also known as the Venturi tube, and the shape of each of the narrowing parts is similar to the shape of a funnel. Pressure in the constricted areas is lower than in the wider parts of the tube. It is important to note that flow nozzle meters and orifice pipe meters work with much better accuracy when the mass flow rate is high, and are not very accurate with low mass flow rate. They are also calibrated based on how much they constrict the flow — a property that changes with wear and tear. Thus, these meters either need regular maintenance or lose accuracy. Despite the tendency of these meters, especially the orifice pipe ones to get damaged easily, especially by corrosive materials, they are very inexpensive to install and use and thus remain popular.

Rotameter diagram. The float marked in orange moves up the vertical tube until it stops, once the forces that push it up and pull it down reach equilibrium. The mass flow rate is determined based on the height at which the float stops moving up.

### Rotameters

Rotameters are also known as **variable area flow meters**. They are considered to be differential flow meters. Two pipes, the incoming and the outgoing ones are connected with a vertical pipe. The incoming pipe is lower than the outgoing pipe. The vertical attachment is narrow at the bottom and wide at the top — the name “variable area flow meter” reflects this design. The difference in diameter creates a pressure difference, just like in the other differential flow meters. A float is placed inside the vertical attachment. On one hand, the fluid that runs through it and its buoyancy cause the float to move upwards. On the other hand, gravity pulls the float down. In the narrower parts of the tube the combination of the forces that push the float up and pull it down results in a force that pushes the float up. As the float propels upwards, the combination of these forces decreases in magnitude with the height increase, and eventually, these forces reach equilibrium and the float stabilizes and stops moving. The height at which the float stops depends on unchangeable factors, such as the float’s weight, the diameter of the tube at each height, and the viscosity and the density of the fluid. It also depends on the variable value for the mass flow rate. If we know the constant factors, we can calculate the mass flow rate given the height of the float. These meters are very accurate and can produce data within the error of 1%.

A Coriolis flow meter. The first image is a side view of the meter, with the two pipes moving towards each other and away from each other. The second and third images are the view from the top, with blue and green being different positions of the pipes in time. Here the blue differs for the two pipes to differentiate them. In picture 2 the pipes are moving towards and away from each other with the same amplitude. In picture 3 the tubes are moving towards and away from each other with a different amplitude because fluid flows through them.

### Coriolis Flow Meters

A demonstration of Coriolis effect using a shower hose. Left — the water is not running. Right — the water is running through the hose. |

Coriolis flow meters depend on the forces that are exerted on the pipes, through which the fluid flows. This meter often splits the fluid flow into two curved pipes. In some cases the pipes are straight, and in other cases the pipes are curved. The two pipes are forced to vibrate with a given amplitude, and their vibrations are synchronized when there is no fluid flowing through them, like in pictures 1 and 2 of the illustration. When the fluid does flow, it changes the amplitude and phase of the oscillation of the pipes and makes their vibrations asynchronous. The phase shift in the oscillations depends on the mass flow rate, therefore collecting data about the oscillations allows us to calculate the mass flow rate.

An illustration of a water hose, shown in bright orange. Light orange shows the alternative positions of the hose as it swings. Picture 1 is a side view, while pictures 2 and 3 are the view from the top. The swinging of the hose without fluid in pictures 1 and 2 is uniform. Fluid flows through the hose in picture 3 and changes the nature of the swing.

We can think of an everyday example to illustrate this behavior. Imagine that you are holding a water hose connected to a pipe. If you start swinging it like a swing while the water turned off, then the motion will be uniform along the part of the hose that is being moved. If we turn on the water, the hose will still move similarly, but it will also start moving in a snake-like pattern.

### Ultrasonic Flow Meters

Ultrasonic flow meters send an ultrasonic wave through the fluid. There are two kinds of meters: Doppler and transit time meters. In **Doppler meters** the initial ultrasonic wave sent through the fluid is then reflected back to the sensor. The difference in frequency between the initial wave and the reflected one is measured, and the difference in frequency increases with the increase in mass flow rate.

Doppler meter. Here the transmitter that sends an ultrasonic signal is marked in orange and labeled A. The signal is reflected and then collected by the receiver B, also marked in orange. Mass flow is determined by the difference in frequency between the signal sent and the signal received.

**Transit time meters** measure the amount of time it takes for a wave to travel with the flow and compare it to the time it takes for the wave to travel against the flow. The greater the difference — the higher the mass flow rate.

The ultrasonic transducers, the reflectors (if used), and the readers do not have to be in direct contact with the fluid, therefore one of the benefits of ultrasonic flow meters is that they do not get damaged easily by the fluid, and can, therefore, be used with hazardous fluids. On the other hand, they cannot be used effectively with fluids, which do not allow easy propagation of ultrasonic waves.

Transit time meter. The orange transmitter and receiver on the top are located upstream, while the orange transmitter and receiver at the bottom are located downstream. The time it takes to send and receive a signal from the upstream to the downstream device is compared to the time needed for sending and receiving the signal from the downstream to the upstream device. The difference between the two increases with the increase in mass flow.

One application for ultrasonic meters is to measure the open flow or flow of water in rivers. The flow of sewage can also be measured this way. This data can be used in environmental assessment, farming (including fish farming), waste management, and in many other applications.

### Conversion to Volumetric Flow Rate

If we know the density of the fluid, we can easily convert the mass flow rate to the volumetric flow rate, and the other way around. Just like mass is found when multiplying density by volume, we can express mass flow rate as a product of volumetric flow rate and the density. When doing these calculations, we have to keep in mind that volume changes with changes in pressure or temperature.

## Applications

Mass flow rate estimations are useful in many industries. For example, mass flow rate is convenient when evaluating water use in private homes. As we saw, we can also measure the open flow of water using mass flow rate. Coriolis and variable area flow meters are also used in wastewater treatment, as well as in mining, pulp and paper industry, power generation, and petrochemical production. Some of these meters, such as the variable area flow meters, can be a part of a larger evaluation system. Aerodynamics is another application for the mass flow rate that we consider in more detail.

### In Aerodynamics

When we consider flight, we can think of air as a liquid moving against the body of the airplane or another vehicle. Of course, it is the airplane that propels forward, and the air does not “fly” past the airplane at considerable speeds, but if we make the airplane our reference point, then we can say that is stationary and the air moves past it. Thus, we can consider the mass flow rate to be one of the properties that affect the “flight” as we see it (the airplane moving relative to Earth).

The four forces acting upon the airplane are lift (B), directed upwards, thrust (A), directed forward towards the movement, weight (C) directed towards the Earth, and drag (D) directed against the movement.

There are several instances when the mass flow rate of the air affects the properties of the flight, and we will consider two situations: the overall flow of air past the airplane that keeps it airborne and allows it to move forward, and the flow of air through the turbines that propels the airplane and creates thrust. First, we will consider the former.

Let us briefly look at the forces that act on the airplane in flight. Some of these forces are complex but describing them in detail is beyond the scope of this article, so we will consider the simplified model. The force directed up and labeled B in our illustration is **lift**.

The force that drags the airplane down as a result of gravity is its **weight**, labeled C. Lift has to overcome the weight for the aircraft to stay in the air. **Drag** is parallel to the movement but acts in the opposite direction. Drag hinders the movement of the aircraft forward. It can be compared to friction for objects that move against a hard surface. On our illustration it is marked D. Finally, the force that propels the aircraft forward is **thrust**. It is generated by the engines, and it has to overcome the drag that acts in the opposite direction. It is marked A on the illustration.

Commercial aircraft like this Boeing 737-700 are designed for best performance at their cruising speed and cruising altitudes.

All of these forces except for weight are affected by the mass flow rate of the air past the aircraft, when we consider the aircraft stationary, as discussed earlier. When deriving the formula to calculate a given force using the mass flow rate, we will see that when all other variables are constant, force is proportional to velocity squared. This means that if we double the velocity, the force will increase 4 times, and if the triple the velocity, then the force will increase 9 times, and so on. This is very useful because it allows us to increase the force that lifts the aircraft by manipulating the aircraft’s velocity, for example. We can also manipulate the velocity of the air that we accelerate when creating thrust, to increase this force, or we could manipulate the mass flow rate instead.

When talking about lift we should note that velocity and mass flow rate are not the only factors for increasing lift. A decrease in air density decreases the lift, therefore to save fuel aircraft have to fly in the air that has density no lower than the specified value, not to hinder lift. This means that there is a limitation on how high aircraft can fly because the higher the altitude — the lower the density. When designing an aircraft engineers take this into account, and so do flight operators that determine the altitudes, at which aircraft fly.

JT15D Pratt & Whitney Canada turbofan engine at Canada Aviation and Space Museum. Turbofan engines are most efficient in the range of speeds 500 to 1000 km/h or 310 to 620 mph.

Now let us consider the second case of the mass of air moving through the turbines to generate thrust. Thrust has to be high enough to ensure that combined with the lift it overcomes the weight and the drag and the aircraft moves forward with a specified velocity. Aircraft engines generate thrust by continually moving large bodies of air over a short distance, using propellers, fans, or turbines. This means that the large mass of air enters the turbines, and is pushed out to travel a short distance away from the turbine. When the air is moved away from the aircraft, the aircraft moves in the opposite direction, according to Newton’s third law. An increase in the mass flow rate increases the thrust.

We could also increase the velocity of the air that we move to increase thrust, but it is more fuel-efficient for commercial aircraft to increase the mass flow rate instead. However, in other types of engines, such as in rockets, it is more efficient to increase velocity.

References

This article was written by Kateryna Yuri

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Online Unit Converters Hydraulics — Fluids

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### Hydraulics — Fluids

**Hydraulics** is a field of applied science and engineering dealing with the mechanical properties of liquids. Hydraulics focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control, and transmission of power by the use of pressurized liquids. **Fluid mechanics** is the branch of physics that studies fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion.

### Mass Flow Rate Converter

In physics and engineering, **mass flow rate** is the mass of a substance which passes through a given surface per unit of time.

Its unit is kilogram per second (kg/s) in SI units, and slug per second or pound per second in US customary and British Imperial units. Mass flow rate is measured by mass flow meters, also known as inertial flow meters.

### Using the Mass Flow Rate Converter Converter

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