Pressure Loss and Head Loss in Fluid Flows

In piping systems and plumbing systems, pressure loss and head loss phenomena are very important parameters. Because they directly affect the power consumption and power requreiements of pumping systems. For example, if you need to transmit a fluid flow into other places with piping systems, you need to strictly calculate the pressure loss through these piping systems. Here, you can find information about these subjects;

• What are pressure loss and head loss?
• How to calculate the pressure and head losses?
• What are the parameters affecting them?
• Examples to understand these phenomenons.
• FAQs

Pressure Loss Due to the Wall Friction

To transmit the fluid through pipes, we need to use a pumping system. Pumps are increasing the energy of the fluid flow to transmit the fluid flow to long distances. Also, we generally use piping systems for these purposes.

Because of the flow inside the pipes, there is wall friction between the fluid and the pipe walls. This wall friction causes losses in the fluid flow energy. So, this fluid flow energy emerges as the pressure loss. There is a pressure of flowing fluid through pipes. But with the increasing distances, this pressure drops. Because of this pressure drop or pressure loss, fluid losses energy, and velocity.

So, we need to calculate the pressure loss effectively for pipe flows.

Pressure Loss Formula for Pipes

We generally calculate the pressure loss for pipes with this formula;

In this formula,

• f is the Darcy friction factor that we calculate it diving the 64 with the Reynolds number of the fluid flow. This calculation is for the circular tubes.
• L is the length of the pipe in meters or ft.
• D is the diameter of the pipe in meters or ft in English units.
• ρ is the density of the flowing fluid in kg/m3 or lb/ft3.
• Vaverage is the average fluid flow velocity in a pipe. The unit is m/s or ft/s.

So the unit of the pressure loss is Newtons or psi.

If you take a look at the equation, there is a direct proportion between the pressure loss and the Darcy friction factor. So, with the increasing Reynolds number which means also turbulence, the pressure loss increases. This means that we decide on more laminar flows in pipes.

Also, with the increasing length of the pipe system, the pressure loss increases. If want to send the fluid in longer distances through pipes, you need to use more pumping power.

There is an inverse relationship between the pressure loss and the diameter of the pipe. Also, if the density of fluid increases, the pressure loss increases. Because high-density fluids have generally more wall frictions.

Also, the average velocity of the fluid has a very big effect. There is an exponential relation between the pressure loss and the average velocity.

Head Loss Due to the Wall Friction

We generally use the head loss term to define pressure loss more easily. The head loss means, the loss of fluid height. There is a pump that sends the fluid to the higher places. There is friction between the piping system and the fluid. So, the average height of the fluid or head of the fluid will decrease for this pump. This is the head loss.

The unit of the head loss is meters or ft. We calculate the head loss with this formula;

As you see here, there are somewhat different parameters. Here, we are not using the density of the fluid. The new parameter is gravitational acceleration. So, the effect of the gravitational acceleration decreases the head loss. But this value is constant.

Average Velocity Calculation

If you know the pressure loss of a system, you can calculate the average velocity in a piping system. You can do it with this formula;

But we use this equation in the calculation of the horizontal tubes. In here;

• ΔP is the total pressure loss,
• µ is the viscosity of the fluid.

So, if the viscosity of the flowing fluid increases, the average velocity decreases. And also, if the diameter of the pipe increases, the velocity of the fluid increases.

The pressure difference has a direct effect on the fluid velocity. Also, with the increasing pipe length, the average velocity increases.

What is the Darcy Friction Factor?

Darcy friction factor is a very important dimensionless value that we use in the head loss and pressure loss calculations. With this factor, we obtain much more accurate results. We are calculating this factor with this formula;

As you see above, the calculation of the Darcy friction factor is very simple. In this formula, Tw is the wall shear stress between the pipe walls and the flowing fluid. So, with the increasing wall shear stress, the Darcy friction factor increases.

But this formula is a general formula for all internal fluid flows. We generally use 64/Re for these calculations.

Pressure and Head Loss Due to the Local Factors

In the design of piping systems, we are not using only pipes. We use elbows and valves etc. Into the pressure and head loss, we need to consider these factors also. Because they provide additional friction and additional pumping power to transmit the fluid.

The calculation of the head loss due to the fitting elements is very simple. We can use this equation for it;

In this equation, the only difference is the K factors of fitting elements. We can use different kinds of elements in a piping system. And all of these elements have K factors which add extra friction. So, the Kfitting elements are the summation of all of these factors.

Total Pressure Loss and Head Loss

So the total head loss is the summation of the head loss due to the wall friction and head loss due to the fitting elements. We can use these formulas to calculate the total losses;

And the total pressure loss;

Total Pressure Loss and Head Loss Calculator

Above all, we prepared a calculator to calculate the pressure loss and head loss of a piping system easily. You will probably deal with lots of these calculations in piping system projects. Check the calculator below.

You can calculate the total pressure and head loss with the addition of K factors of local elements and wall friction factors.

Total Pressure and Head Loss Calculator

Reynolds Number:

Pipe Length :

Pipe Diameter :

Density:

Average Velocity :

Total K Factor :

Darcy Friction Factor =

Total Pressure Loss =

Total Head Loss =

The use of the calculator above is very simple. Firstly, you just need to enter these values;

• Reynolds Number: Dimensionless unit
• Pipe Length: In meters
• Pipe Diameter: In meters
• Density: kg/m3
• Average Velocity: m/s
• Total K Factor: Dimensionless

Once you entered these values, click on the ‘Calculate!’ button to see these results;

• Darcy Friction Factor: Dimensionless
• Total Pressure Loss: Pascals
• Total Head Loss: Meters

If you want to make further calculations, click on the Reset button. And then re-enter the values.

Conclusion

So, the calculations of pressure loss and head loss are very important in the design of piping and pumping systems.

There are generally two factors that lead to a head loss on a system. The wall friction and the other fitting elements. We add the effects of fitting elements such as elbows and valves as the K factors.

Above all, Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

Also, You can find out much more calculators like this in Mechanicalland! Take a look at the other engineering calculators available in Mechanicalland!

Finally, do not forget to leave your comments and questions below about head loss and pressure loss.

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