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## Stagnation vs. Static Pressure

Pressure definitions are at times ambiguous when performing calculations. AFT software is equipped to handle each definition presented for the user. Stagnation pressure is also known as total pressure and accounts for the dynamic pressure and the static pressure. This is best represented with a pitot tube pointed into the direction of flow. The static pressure does not consider any buildup of pressure resulting from local velocities and is represented with a pressure tap normal to flow. Assigned pressure junctions allow users to specify which pressure definition they would like to use. Mid-pipeline applications will use static properties, while reservoirs or similar boundary conditions are best modeled with stagnation properties.

## Difference Between Stagnation Pressure and Static Pressure

When fluid flows, it experiences two kinds of pressures, static and dynamic pressures. Static Pressure is the pressure at a point in a fluid. It is the actual thermodynamic pressure of the fluid. It doesn’t take into account the flow of fluid. Stagnation pressure is the pressure the fluid would obtain if brought to rest without loss of mechanical energy. The difference between the two is the Dynamic Pressure (or velocity pressure) and is a measure of the fluid speed.

Static Pressure is represented by the term P of Bernoulli’s equation. The sum of static and dynamic pressures acting on the fluid element is termed as stagnation or total pressure.

Ρ sta= Ρ sta+ Ρ dynamic

Resources There's often confusion when deciding whether to use static pressure or stagnation pressure. This frequently arises when defining a pressure within a control valve junction or an assigned pressure Junction. This also arises when reviewing pressures in the output. What's the difference between static pressure and stagnation pressure? This can best be illustrated by breaking down the Bernoulli equation into its components.

The Bernoulli equation states that for incompressible inviscid flow, the sum of static pressure plus dynamic pressure plus hydro static pressure remains constant along a streamline stagnation pressure is the sum of static pressure plus dynamic pressure

To better illustrate the relationship between static pressure, dynamic pressure, and stagnation pressure, the video above reviews an open tank draining through a pipe due to gravity. The graph in the video shows the stagnation pressure and static pressure plotted against the flow length. Keep in mind that stagnation pressure is always greater than or equal to static pressure.

The static pressure at location 1 is equal to the stagnation pressure at location 1 since the velocity or dynamic pressure at location 1 is essentially zero. Likewise, the static pressure location 2 is equal to the stagnation pressure at location 2 since the velocity at location 2 is essentially zero. The static pressure and stagnation pressure between locations 1 & 2 only varies due to the change in hydrostatic pressure at location 3. We will assume a lossless connection to simplify this discussion at this point our stagnation pressure is the same as at location 2.

However, our dynamic pressure has increased due to the introduction of velocity to the fluid. The increase in velocity means there is now a dynamic component to account for. Notice in the graph at location 3 that the static pressure decreases. The amount by which the static pressure decreases is equivalent to the amount of dynamic pressure introduced as fluid moves along the pipe from location 3 to location 4. There is a decrease in stagnation pressure due to friction. This pressure loss is irrecoverable while the decrease in static pressure has both recoverable and irrecoverable components.

Notice that as fluid moves through the area expansion at location 4 again, we will assume that this is a lossless component. The static pressure increases due to the decrease in fluid velocity it is worth reiterating that stagnation pressure is always greater than or equal to static pressure.

Notice that at locations 3 & 4 where the fluid velocity changes, the stagnation pressure does not change except for losses due to friction. Now let's take a look at how this comes into play when defining your system. The control valve Junction is one of two junctions in the toolbox which requires you to specify either a static or stagnation pressure. Most real-world control valves read system pressures using a sensor connected to a tap in the side of a pipe. Unless the pressure sensor has an inline element such as a pedo 2, the pressure reading will return a static pressure measurement by default.

Our control valve pressure set points are set to control on a static pressure. The assigned pressure Junction is the second Junction that requires you to specify either a static or stagnation pressure the assigned pressure Junction acts as a system boundary. This Junction will not balance mass flow into and out of itself. Instead, this Junction will source and sync whatever flow is required to maintain the user-defined pressure. Defining this Junction using a stagnation pressure is appropriate when trying to model a large body of fluid with negligible velocity. Defining this Junction using a static pressure is appropriate. For example, when defining a custody transfer in a pipeline if you are modeling a system up to the point of a custody exchange, it is likely that you have a flow element and a pressure gauge at that point. You would then either define your system boundary using an assigned flow Junction or, assuming there is not an inline pressure sensor, you would use a static pressure system boundary.

It is equally important to be aware of which parameters you are reviewing in the output if you are comparing the results of your model to actual pressure measurements from your system. Be sure to compare a static pressure gauge measurement to a static pressure output parameter. Dynamic pressure is a very useful output parameter for understanding the difference between static pressure and stagnation pressure as dynamic pressure is simply stagnation pressure - static pressure. Another common source of confusion is how to define a discharge system boundary. As specified by Crane Technical Paper, for 10a k factor of 1 should be applied to an abrupt transition pipe exit. The confusion arises when defining a discharge pressure in association with a discharge loss coefficient. When discharging into a reservoir or a large body of liquid where the velocity is essentially 0, eft recommends that the user always define a stagnation system boundary. The three systems on the Left are all defined the same except for the discharge system boundary for this simple comparison we are modeling water at 59 degrees Fahrenheit. Flowing from a pressure of 20 psi a stagnation through 20 feet of 2-inch pipe into the base of a reservoir that's 10 feet deep. J-10 is a reservoir junction with a 10-foot liquid surface elevation in the pipe depth and loss coefficient tab we have to find the pipe depth to be 10 feet below the surface elevation and a pipe exit loss coefficient of K equals 1 to represent an abrupt pipe exit per crane

J-20 is an assigned pressure junction which is representing the same boundary condition as j-10. To do this, we need to first convert 10 feet of water into a pressure

As we are assuming this system boundary is a large body of water with a negligible velocity, we will define this Junction using a stagnation pressure. When defining a system boundary using a stagnation pressure you must manually account for a loss coefficient. Again, this system boundary will be modeled using an abrupt transition pipe exit loss as defined by Crane.

Notice how the results of these two systems are the same except for a slight difference? Due to converting 10 feet of water to 4.33 to PSIG, j30 is also an assign pressure junction and will be representing the same system boundary condition as J 10 and J 20. This Junction has been defined using a static pressure. Again, this pressure is equivalent 10 feet of water, however when you specify this pressure as static you do not need to account for the pipe exit loss coefficient. You can see that the results for this system are the same as the previous two systems. When modeling a system boundary using a static pressure, you are intrinsically accounting for the K equals one exit loss. That represents an abrupt transition pipe exit used with a stagnation pressure. Although this may appear to simplify the modeling process, it can complicate things when using the loss coefficient for something other than an abrupt transition pipe exit. A stagnation pressure boundary condition will simplify your model if you have a loss coefficient other than K equals one. If you plan on evaluating multiple system operating conditions, we will elaborate on the relationship between changing system operating conditions and system boundary definitions along with appropriately representing pressure measurements in a future tutorial.

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