Flow Work – Flow Energy of a Flowing Fluid

Flowing fluids are very important in our lives. Maybe lots of people can visualize flowing fluids as rivers or water coming from a tap. But, this phenomenon is a very important side. There is a term that we call flow work. Here, we explain the general aspects of this term. Here, you can find information about these topics;

  • What is flow work? Hot to calculate it?
  • What is the energy of flowing fluids?
  • Energy conservation in steady flow systems.
  • Devices and machinery that we use flow work.
  • FAQs about this term.

What is Flow Work?

In general engineering devices, we can see this phenomenon. So, flow work is the total work that we do while forcing the fluid to flow.

The calculation of the flow work for unit mass is very simple. You can use this formula;

Flow work formula.

So, this equation is giving results on the kj per kg basis. So, if you multiply this with mass, you can find the total energy. In this equation;

  • P is the total pressure o push the fluid mass. The unis are Pascals or psi.
  • v is the specific volume of the fluid that we push. The unit is m2/kg or ft3/lbs.

In such cases, we need to calculate the total energy of a flowing fluid. So, flowing energy is one portion of this total energy. We can calculate the total energy with this formula also;

The total energy of a fluid.

According to this equation, we considered the internal energy, kinetic energy, and potential energy of the flowing fluid. Also in this equation;

Pv is the total energy of the flowing fluid,

u is the internal energy,

ke is the kinetic energy,

pe is the potential energy.

Also, we can write this total energy equation in this form;

Total energy calculations.

This is the last form of the total energy of a flowing fluid.

h means enthalpy which equals the flow energy + internal energy. V is the velocity of the fluid flow which we require in the calculation of kinetic energy. Also, z is the elevation of the fluid in feet or meters.

And g is the gravitational constant acceleration value.

Energy Transport of Flowing Fluids

So, the importance of the flow works emergers in here. In most engineering systems, we calculate the total energy transport of fluid. We use this energy in different means. So, we can calculate this energy with this formula;

Flow energy.

As you see above, it is very simple to calculate the total energy transport of a flowing fluid. You just need to multiply the total energy with mass. Or, if you multiply this energy value by the mass flow rate, you will have;

Flow energy in formular basis.

This is the general equation that is important for us in the flow energy calculations of engineering devices.

Energy Balance on Flow Work for Flowing Fluids

If we think about a control volume system, we need to consider the work output done by the system and the total heat that comes inside the system. Also, we can assume that there is an inlet fluid flow and outlet fluid flow in this system. So, we can think about the general thermodynamical systems in terms of this approach. The total energy balance of these systems is like this;

Energy balance in flowing fluids.

This equation may seem very complex, but it is not. We use the Q as the total heat input or output from the control volume. This can occur because of the heat input of the flowing fluid or chemical reactions. Also, we denote the total work input or output to the control system as W.

So, the difference between these two values is equal to the difference between the total input flow energy and the output flow energy. This is the most general equation that we can use for most engineering devices.

Rate of Heat Transfer

We donated it as Q. This is the total rate of heat transfer between the walls of the control volume and surroundings. If there is complete insulation, we need to consider this value as 0. Also, if the total heat transfer is to the outside region of the control volume, we assume this energy as negative.

Power of the Devices

W is simply the power of the devices. It is directly related to the total energy change of the enthalpy of the fluid that comes inside the control volume and goes outside of the control volume. For most engineering devices, this is the shaft power. If you can understand this relation, it will very basic for you how the general engineering devices are working.

Total Enthalpy Change

Total enthalpy change of the flowing fluid is a common cause of the working of the engineering devices. The enthalpy of the inlet fluid and the outlet fluids are important in these calculations. We can find the enthalpies of fluid from the general thermodynamical tables.

This is the general situation of engineering devices. So, the total enthalpy change is very important. Flow work and flow energy are inside the enthalpy

Change in Kinetic Energy

There are lots of kinds of engineering devices are using the kinetic energies of the flowing fluids. For example, turbines. Kinetic energies of flowing fluids are converted into electric energies in these systems.

If the entering velocity is equal to the output velocity of the flowing fluid, the total kinetic energy change is 0. Also, in most of the systems, the total kinetic energy is very small if we compare it with enthalpy. So in general, we assume that the kinetic energy change of the fluid flow is zero.

Change in Potential Energy

Also, lots of devices are using the elevation difference between the two states of fluids. For example, the hydroelectric power plants, stagnant water from very high elevations comes into the turbine systems of the hydroelectric power plant. This flowing energy is converted into shaft power.

But, the general elevation change is zero in most of the devices. For example, in a heat exchanger, the total elevation change is negligible in general. So, we do not need to consider the equations.

Engineering Devices That We Use Flow Work and Flow Energy

We use these equations in lots of kinds of engineering devices. Energy balance is a very important term and the general efficiencies of the devices and machines depend on the energy balance of the systems. Let’s take a look at the general engineering systems that we use flow work and flow energy equations.

Flow Work and Flow Energy in Diffusers and Nozzles

Nozzle and diffuser.
Image Source: Researchgate.com.

Diffusors and nozzles are very important devices and systems that we use in jet engines, aerospace engine applications, and power plant systems. Even we have hoses that we use these systems.

They are the devices that make an exchange between the flow energy of the fluid and the velocity. In nozzles, the total flow energy and flow work are converted into velocity. So, the velocity of the fluid increases with nozzles But, the total enthalpy of the fluid decreases.

Also in diffusers, the velocity of the fluid decreases, but the flow energy of the fluid increases.

If we make an energy balance analysis for diffusers and nozzles, the general change of the potential energy is zero. So, we do not need to use potential energy change in the energy balance. Also, the total heat transfer change is zero. Because there is no time for the heat exchange between the flow and the surroundings in these systems.

And there is no total work in these devices. So, W = 0.

But there is a change in velocity. So, we need to consider the kinetic energy. Also, the total enthalpy changes. And we need to consider the total enthalpy change. This will be the only energy balance and fluid work in diffusers and nozzles;

Turbines, Pumps, and Compressors

Turbine vanes.
Image Source: Wikipedia.

They are also very important engineering devices that we use in lots of kinds of applications. They have generally the same working principles. But their general purposes are not the same.

We use the turbine systems to generate shaft work from the flow work of a fluid. So, the fluid flows at a rate of mass and velocity. And this fluid flow goes through the turbine wings. The wing rotates with this flow and we produce shaft work. So, there is a work output in turbine systems.

Also in pumps and compressors, we increase the pressure of the fluid. So, there is a work input to these systems to pressurize the fluids. The enthalpy of the fluid increases in pump and compressor systems because of the work input through pump and compressor shafts and vanes.

The only difference between the pumps and compressors is, that compressors are using gases and pumps are using incompressible fluids such as liquids.

Furthermore, there are fan systems that increase the velocities of the flowing fluids. Also, there is a work input in these systems. But the only difference between these fan systems from compressors and pumps, they increase the velocity of the fluid.


For all of these systems, we are using the flow work and flow energy balance equations. Firstly, we need to state that the total heat transfer in these systems is negligible. Because there is no heat transfer between the devices and the fluids inside them.

Furthermore, the total potential energy change of the fluids inside these systems is zero. Because there is no net change in the elevation of the flowing fluids in these systems.

Also, we assume that the total kinetic energy change in these systems is zero. Maybe you can think that there is a total velocity change in the turbines. But the general cause of this velocity change is because of the change in the flow work.

So, we can assume the general formula for these systems;

Throttling Valves

Throttling Valve.
Image Source: Power Magazine.

They are also very important parts of many engineering devices such as air conditioners and refrigerators. We use the throttling valves to decrease the pressure of the flowing fluids. Like nozzles and diffusers, they are very simple mechanisms.

In throttling valves, the total change is about the enthalpy of the flowing fluid. The other factors are not affected. So, the total kinetic energy, and potential energy changes are zero. Also, there is no work input or output for these systems. So the total change in work is zero for throttling valves.

And also, there is no heat transfer between the fluid and the surrounding in these systems. So, we can think that the total heat transfer is zero.

Pressure drop of the flowing fluid takes place in the decrement in the flow every or flow work which was Pv. This decrement is compensated in the increment in the internal energy of the fluid which takes place as the temperature rise.

Also, the enthalpy was the summation of the flowing fluid work and the internal energy. And the total enthalpy change in these systems is zero.

Mixing Chambers

There are lots of kinds of applications in engineering that we can call mixing chambers. In these systems, two or more sources of inlet fluids in different energy states are mixed. And they go from an outlet in the mixed state.

So, we can build an energy balance between these fluids. In these systems, there is no total work that the system does or output work. We can say that the W = 0. Also in these systems, there is no considerable heat transfer. So, Q = 0. And also, there is no net change in the potential and kinetic energies of the fluids.

Like the throttling valves, we can build an equation between the total inlet and outlet enthalpies of the fluids.

Heat Exchangers

Heat exchanger.
Inside of a heat exchanger.

Heat exchangers are very important devices that we use in the heating systems of buildings and industrial machinery. Also, the energy balance calculations are very important for them.

The general working principle of the heat exchangers is very simple. There are inlet and outlet pipes in heat exchanger systems. There is an inlet flow into the chamber of the heat exchanger. And this chamber filled with this fluid. Also, there is an outlet flow of this chamfer where the heated fluid leaves the chamber.

And there is a piping system in the heat exchangers. In this piping system, there is a fluid flow. So, heat transfer between the piping system and the heat exchanger chamber takes place.

If we generally think about this system, there is no net work interaction between the device and the fluid flow work. So we can say the W = 0. Also, the change of the kinetic and potential energies is zero in heat exchangers. We can say that Pe = Ke = 0.

If we think of the heat exchanger chamber as the system, the total heat transfer between the surroundings and the control volume is zero. So, Q =0.

Only heat transfer takes place between the inlet and outlet flow masses. And we need to build the energy balance between these inlet and outlet flows.

Pipe Flows

We explained the general engineering systems that we use in our daily systems. But also, considering the flows in pipes is very important. Because there are lots of heat interactions in the pipe flows.

Flow work is very important in pipe flows. So, we need to consider it.

In a pipe flow, the total energy of the fluid can change because of different reasons. Also, we need to select the control volume. Which section of the pipe will be the control volume is the prime interest.

Kinetic and potential energies can vary in the pipe flow. For example, if you selected a very long pipe section, kinetic energy can decrease because of the wall friction. Also, if the pipe is in the vertical direction, the potential energy can change.

Also, there can be work interactions in pipe flow. Think about a wiring system in a pipe. Electric can be given to these wires and the electrical work is applied to the flowing fluid.

And also, there can be heat transfer between the pipe and the surrounding mediums. If the insulation of the pipe is not good enough to prevent heat losses, we need to consider the total heat transfer.

As you see above, the analysis of the pipe flow can change according to the piping system. In general engineering systems, we need to make the energy balance analyses in different means.

What Happens in Unsteady Systems?

Unsteady flow systems are very common also. In these systems, the flow regime is not steady like the engineering systems above. The flow regime can vary with time. So, we can not use the mass flow rate approach for these systems.

We call these unsteady systems because of the flow regime that we have. The flow regime is a very important parameter in the calculation of the energy balance and the flow work and flows energy.

For example, think about a chamber filled with fluid with a valve. So, the opening and closing of this valve will lead to an unsteady regime. And we need to think that, how many times and how much time this valve stays open in this regime. We can make our calculations according to this approach.

Also, we can use time-averaged calculations. We can assume the regime as a time-averaged system to make the general flow work and flow energy calculations.

Conclusion on Flow Work and Flow Energy

Flow energy and flow work in engineering are very important. They directly affect the total energy balance in engineering systems. We use the fluid flows in different engineering applications and the energy balance calculations of these fluid flows are very important.

It is also very important a proper selection of the control volume. We are doing our steady and unsteady flow work and flow energy calculations according to the selection of the proper control volume.

Also, there are lots of kinds of devices that we use the energy balances between the different parameters that we stated above. Around these devices, compressors, and pumps make the energy conversions between the mechanical energy and fluid flow work. Valves, diffusers, and nozzles that do not make any work and heat output and input.

Do not forget to leave your comments and questions below about the flow work and flow energy.

Your precious feedbacks are very important to us.

FAQs About Flow Work and Flow Energy

What is flow work in thermodynamics?

The flow work is the required work energy to push a portion of the fluid in a system. This phenomenon is very important in lots of engineering systems. We use these calculations to calculate the total efficiencies of the systems.

How to calculate the flow work?

It is very easy to calculate it. You just need to multiply the pressure of the fluid by its specific gravity of it. You can think of it as a piston that pushes the fluid inside a pipe or cylinder. So, specific gravity and pressure are the most important factors to calculate the flow work.

What is the flow energy of fluids? 

Fluid flows are also very important in engineering systems. Also, they consist of a type of energy that is required to flow over a surface or inside pipes. This energy is the flow energy of the fluids. In Bernoulli’s equation, flow energy is a very important stuff that we calculate.

Where do we use flow work calculations?

There are different kinds of engineering systems that we use the flow work calculations. The most common applications; are heat exchangers, throttle valves, diffusers and nozzles, mixing chambers, pipe flows, compressors, pumps, and turbines. So, these calculations are very common in engineering.

What is the difference between the flow work and displacement work?

For flow work, we need to have continuous flow over a control volume. After that, we can make the flow work calculations. But in displacement work calculations, we do not have any control volume to calculate the flow.

What is the unit of the flow work?

The general unit of the flow work is the same as the unit of the work. The unit is kJ or BTU in English units.


Leave a Reply

Your email address will not be published. Required fields are marked *