13 replies to this topic

[samin_chemeng]

Hello,

 

I’ve encountered a process modeling problem involving the mixing of two incompressible liquid streams with different pressures and pipe diameters. While it seems straightforward, I haven’t found a clear analytical solution or theoretical justification for how the pressure behaves at the mixing node. Most process simulators (e.g., Aspen HYSYS) assume that the pressure at the mixing point is equal to the minimum of the two inlet pressures, but I would like to understand whether this is physically justified or just a modeling convention.

 

Here’s the setup:

• Stream C1:
  Volumetric flow rate: Gv1 = 200 m³/h
  Pressure: P1 = 10.5 barg
  Pipe diameter: D1 = 200 mm, L1 = 400 m;

• Stream C2:
  Volumetric flow rate: Gv2 = 100 m³/h
  Pressure: P2 = 3.5 barg
  Pipe diameter: D2 = 100 mm, L2 = 10 m;

• The two streams mix at node N1, forming stream C3 with:
  Flow rate: Gv3 = Gv1 + Gv2 = 300 m³/h
  Pressure: P3 = ?
  Pipe diameter: D3 = 200 mm, L3 = 85 m;

• The mixed stream flows to a discharge point U1 (e.g., a tank) with pressure:
  P4 = 1.03 barg (hydrostatic)

In the simulator, the pressure at the mixing node appears to be P3 = min(P1, P2) = 3.5 barg, and the excess energy seems to be reflected in a slight increase in fluid temperature. I attempted to apply Bernoulli’s equation, but I’m unsure whether it’s valid in this context, especially since the mixing occurs at a junction and not along a single streamline. Also, I’m not sure if I’ve accounted correctly for the energy losses or the state functions of the fluid (incompressible liquid in this case).

 

In my analysis, I used the following energy balance:

Before mixing:
Gv1 × (h1 - F1) + Gv2 × (h2 - F2) = Gv3 × h3

After mixing and before discharge:
Gv3 × (h3 - F3) = Gv4 × h4 → h3 - F3 = h4

Where:
Gv = volumetric flow rate [m³/h]
P = pressure [barg]
D = pipe diameter [mm]

L = pipe length [m]
h = specific enthalpy [kJ/kg]
F = specific energy loss due to friction [kJ/kg]
η = kinematic viscosity [cP]
ρ = density [kg/m³]

 

My question is:
Is there a theoretical basis for assuming that the pressure at the mixing node is equal to the lower of the two inlet pressures, especially when the pipe diameters differ? Or is this simply a modeling simplification used in simulators?

Any references to literature, textbooks, or articles that address this type of hydraulic mixing behavior would be greatly appreciated.

Thank you in advance!

[Pilesar]

Fluid pressure at the mixing node is calculated backwards from the sink. There is just one combined stream after mixing. If you know the flow rate and the final sink pressure, it is just a matter of determining the pressure drop to the sink to find the pressure at the node.

  In every case I have seen, fluid moves from high pressure to low pressure unless mechanically acted upon (for example, by a pump or compressor.)

  Your pressure at P3 will NOT be as high as P1 or P2. There will be pressure drop caused by the piping between the source and the mixing node. Do not ignore the pipe lengths!

  Your problem statement is really over specified with at least three equations. Any one of the three streams can be used to calculate the pressure at the mixing node. They should each give the same answer since there is only one unique pressure at P3. When calculating pressure drop through a pipe, there are additional unstated parameters that matter. Elevation change and pipe roughness are not given. In real life, pipe roughness is assumed or backwards calculated from measured pressure drop as a tuning parameter. I suggest you calculate the pressure drop of all three streams separately as if they were completely independent as an exercise even though just the stream from P3 to P4 is adequate to find the solution.

[katmar]

I agree completely with Pilesar. About the only thing that correlates with the minimum of the two supply pressures is that if the pressure at the node is higher than the minimum of the two inlet pressures then the flow in the line from the lower pressure source will reverse and flow towards the source (assuming that there are no changes in elevation).

[latexman]

When two liquids are mixed, the pressure at the mixing point will equalize and, in a continuous flow system, the resulting pressure will be at or below the lowest pressure of the incoming streams.

The simulator rule is spot on.

[astro]

If you're after an old school analysis of your question, then the paper by Zenz - Minimise Manifold Pressure Drop, Hydrocarbon Processing, Dec 1962, Vol. 41, No. 12, pp.125-130, is worth a look.

 

Another port of call is to lay your hands on Idelchik, Handbook of Hydraulic Resistance, 4th Ed., 2007. The 7th chapter is devoted to this question.

 

For a shorter, simpler and up to date review of the subject, recent editions of Crane's TP410 Flow of Fluids, provides another perspective.

 

A manifold is, in simple terms, a bunch tees joined together in close succession. Understanding the hydraulics of tees, wyes and manifolds is a long standing challenge in our profession. The ultimate goal being even flow distribution. This is a worthwhile question to ask and investigate.

 

To quote Idelchik (reference noted above) - effectively reiterating previous discussion but using different narrative:

 

Ch. 7 Resistance in the Cases of Merging of Flow Streams and Division into Flow Streams

7.1 Explanations and Practical Recommendations

4. When two streams moving in the same direction, but with different velocities, merge (Figure 7.1a), turbulent mixing of streams (a shock) usually occurs, which is accompanied by nonrecoverable total pressure losses. In the course of this mixing, momentum exchange takes place between the particles of the medium moving with different velocities. This exchange favours equalisation of the flow velocity field. In this case, the jet with higher velocity loses a part of its kinetic energy by transmitting it to the slower moving jet.

 

 

 Idelchik Fig 7.1a.png   31.58KB   0 downloads

 

The chapter runs for about 100 pages, so it's a dense subject when investigated in detail.

 

[breizh]

Hi,

Let me add other books, easier to read,

Pipe flow a practical and comprehensive guide 

by D Rennels and H Hudson, published by Willey

Flow resistance A design guide for Engineers by E Fried and I.E Idelchick 

take a look at this video

What happens when you mix different pressures?

 

Good luck,

Breizh

[katmar]

When two liquids are mixed, the pressure at the mixing point will equalize...

 

Yes, there can only be one pressure at a point node.

 

 

in a continuous flow system, the resulting pressure will be at or below the lowest pressure of the incoming streams.

The simulator rule is spot on.

 

We need to state the proviso that this is only true if there is flow from the lower pressure source.  Fluids only flow from a higher pressure zone to a lower pressure zone so the pressure at the node has to be lower than both the source pressures if there is flow from both sources. Indeed, the problem statement here does state that there is flow from both sources but as Pilesar pointed out this problem is over specified and the situation cannot occur unless there is equipment other than just the pipes that are causing pressure drops.

 

So I would agree that if the pressures and flows are as stated by the OP then the pressure at the node must be less than the minimum of the two sources but we cannot generalize this to say that the pressure at a node is always limited to this minimum.  As I said before, it is possible to have a reverse flow in one of the branches - although that is not the case here because the problem is over specified.

[latexman]

 

in a continuous flow system, the resulting pressure will be at or below the lowest pressure of the incoming streams.

The simulator rule is spot on.

 

We need to state the proviso that this is only true if there is flow from the lower pressure source.  Fluids only flow from a higher pressure zone to a lower pressure zone so the pressure at the node has to be lower than both the source pressures if there is flow from both sources. Indeed, the problem statement here does state that there is flow from both sources but as Pilesar pointed out this problem is over specified and the situation cannot occur unless there is equipment other than just the pipes that are causing pressure drops.

 

So I would agree that if the pressures and flows are as stated by the OP then the pressure at the node must be less than the minimum of the two sources but we cannot generalize this to say that the pressure at a node is always limited to this minimum.  As I said before, it is possible to have a reverse flow in one of the branches - although that is not the case here because the problem is over specified.

 

Agree.

[samin_chemeng]

Hi everyone,

Thanks a lot for your answers to my question. Your explanations helped me understand that the pressure at the node is determined by the overall hydraulic balance and not just by taking the minimum inlet pressure, even though simulators often use that as a shortcut.

 

Here’s a bit more context from my side:

I have a pump (100-P10) feeding another pump (200-P1), which sends the fluid through a heat exchanger train and then through a flow control valve to UNIT 200.
Right now, 200-P1 discharges at about 15.5–16.0 barg, which is above the design limit of the downstream line (14.0 barg). The safety valve is set at 16.0 barg and vents to an open funnel, which is a burn hazard for operators.
To reduce the discharge pressure, I’m planning to install a control valve on a recirculation line, set to 3.5 barg at its location. After about 1.5 bar pressure drop over 300 m, the suction of 200-P1 would be around 2.0 barg, which should help bring the discharge pressure down.

The tricky part: the same product also comes from another unit at 10.5 barg, controlled by a level control valve upstream. This line runs close to our discharge line, so combining them would save costs.
My concern is how the flows will interact when connected, since UNIT 200 flow is process-driven and the other unit’s flow is level-controlled. In extreme cases, the recirculation flow can reach 100 m³/h when UNIT 200 runs at minimum load (normally it’s around 145–150 m³/h).

Your advice about calculating pressure from the sink backward and considering all pressure drops was really helpful. I’ll also check Idelchik, Crane TP410, and the Zenz paper as you suggested.

Thanks again for your guidance!

 

I’m also considering (after discussing with my former professor) an alternative: redirecting the recirculation flow from the discharge of pump 348-200DP10A,R back to its suction line, closer to the tank (not near the pump). This would create an internal loop to control pressure without interacting with the other unit.

 

Regarding the energy balance, I considered:

 

From a hydraulic perspective, the energy balance can be expressed as:

h = P/ρ + w²/2

where:

• P = pressure
• ρ = fluid density
• w = velocity

The friction losses can be represented as:

F = (λ·L/d + Σξ) · w²/2

where:

• λ = friction factor
• L/d = pipe length-to-diameter ratio
• Σξ = sum of local resistance coefficients

The friction factor λ depends on the flow regime (Reynolds number):

• Laminar: Hagen–Poiseuille
• Transitional: Nian Cheng correlation
• Turbulent: Swamee–Jain equation

Edited by samin_chemeng, 03 October 2025 - 08:40 AM.

[breizh]

Hi Samin,

To save your time and avoid misunderstanding, provide a sketch (PID or PFD). This is the way Engineers work. 

Regarding your last paragraph about friction factors, consider using a correlation which covers the full range of Reynolds. 

See doc attached.

 

About your sets of equations you must provide units, this will help you to correct them.  

note:

Darcy–Weisbach equation - Wikipedia

Breizh 

Attached Files

•  friction factor new model.pdf   1.71MB   4 downloads
•  Minor Losses.pdf   259.79KB   1 downloads

[astro]

Hi,

Let me add other books, easier to read,

Pipe flow a practical and comprehensive guide 

by D Rennels and H Hudson, published by Willey

Flow resistance A design guide for Engineers by E Fried and I.E Idelchick 

take a look at this video

What happens when you mix different pressures?

 

Good luck,

Breizh

Excellent use of youtube breizh. What Process with Pat said.

Edited by astro, 04 October 2025 - 07:02 AM.

[samin_chemeng]

Hello Breizh and everyone,

 

First off, thank you so much for all the help you’ve given me so far. I really appreciate it!

 

Breizh, I took your advice and made a PFD for the proposed recirculation line from 100-P10A,B (Stream 3), which I’ve attached for you to see. I’d love to get your thoughts on my latest update.

 

Process Flow Diagram for proposed situation

 PROCESS FLOW DIAGRAM.pdf   419.59KB   26 downloads

 

What I’m Trying to Do (proposed situation)

I think adding valves 300-FV-02 and 100-PV-03 could work. Here’s the plan:

• Loop 03 (PC-03 → PY-03 → PV-03): This is pressure-controlled and will cause a pressure drop (ΔP1).
• Loop 02 (LEVEL CONTROL → FC-02 → FY-02 → FV-02): This is flow-controlled and will cause a pressure drop (ΔP2).

The idea is to balance things so that 10.5 barg - ΔP2 = 3.5 barg - ΔP1. But since one loop is flow-driven and the other is pressure-driven, I’m worried about how they’ll play together at the mixing node.

What I Found with the Simulation

I ran a simulation in Autodesk CFD, using an incompressible fluid, turbulent flow, the ADV 5 advection scheme, and keeping it isothermal. Here’s the setup:

• Stream 13 (Inlet 1): 200 m³/h, velocity 1.77 m/s, pipe length 400 m.
• Stream 3 (Inlet 2): 100 m³/h, velocity 3.54 m/s, pipe length 5 m.
• Outlet 1 (Sink): Pressure set to 1.03 barg.

I checked the velocity and pressure at a cut Z = D/2 = 0.1 m and got these numbers:

• Face Inlet 1 (Stream 13): P1 = 4.9825 barg.

Autodesk CFD Plan section at inlet 1

 profile at inlet 1.pdf   282.41KB   9 downloads

• Face Inlet 2 (Stream 3): P2 = 2.732 barg.

Autodesk CFD Plan section at inlet 2

 profile at inlet 2.pdf   273.17KB   1 downloads

• Mixing Node (N1): P3 = 2.5 barg.

Autodesk CFD Plan section at mixing node

 profile at mixing node.pdf   341.87KB   5 downloads

• Face Outlet 1 (Sink): P4 = 0.977 barg.

Autodesk CFD Plan section at sink

 profile at sink.pdf   283.75KB   7 downloads

 

The attached pictures show the velocity and pressure profiles at Z = D/2 = 0.1 m for the mixing node, Inlet 1, Inlet 2, and Outlet 1.

 

1. Does the pressure at the mixing node (P3 = 2.5 barg) make sense with the flow and pressure controls I’m using?
2. How can I make the flow-driven and pressure-driven loops work well together?
3. Would it be better to redirect the recirculation from 200-P1’s discharge back to its suction near the tank instead of mixing it with the other stream?

I also did a simulation with following settings & boundary conditions:

 

• Stream 13 (Inlet 1): pressure 10.5 barg (pipe length 400 m).
• Stream 3 (Inlet 2): pressure 3.5 barg, pipe length 5 m.
• Outlet 1 (Sink): Pressure set to 1.00 barg.

And I got the following results:

 

At plane XZ = -0.5m from mixing node, I got avg(V) = 1.51 m/s, flow Gv = 33.6m3/h with pressure P = 3.43 barg

At plane YZ = 400.5 m from inlet 1 face (0.5m after mixing node in y directions towards sink), I got avg(V) = 3.03 m/s, flow Gv = 262.4m3/h with pressure P = 3.37 barg

 

 P1=10.5barg_P2=3.5barg_P4=1.0barg.png   134.06KB   0 downloads

 

I’d be grateful for any suggestions or pointers to help me figure this out.

 

Thanks again!

 

Edited by samin_chemeng, 05 October 2025 - 09:07 PM.

[breizh]

Thanks for sharing your PID.

 

Better to recycle to the storage tank and use its buffer capability.

EDIT: Modification were performed yesterday but not taken into account?

Use the storage tank as a buffer and mixing tank. Consider bringing the feed stream together with the recycling stream back to the tank.

Install an LCV on the feed stream associated with a LICA on the storage tank, Add 2 LS (H&L) to prevent overflow and cavitation of the pump.

On the discharge of the pump install a FIC associated with a FCV to control the flow rate to the HX.

 

Share with us info about the pipe material, product (nature, density, viscosity, temperature) to perform minimum calculation.

 

 

Regarding your software/CFD I cannot comment.  

 

Breizh 

[astro]

A couple of off the cuff comments from me:

1. I would simplify the flow scheme and opt for a single pump set up rather than pumps in series (various benefits in terms of operations, maintenance and reliability). Assuming the pumps are fixed speed, centrifugal types, then 100-P10A/B is/are covered in some way for minimum flow protection. However 200-P1A/B is/are not. In the event of a downstream flow restriction (anywhere along the heat exchanger train and off "To Plant"), 200-P1A/B will be starved of flow and prone to damage.
2. Pressure control to work minimum flow protection on 100-P10A/B is reasonable by specifying the the set point of PC-03 to a margin above the normal discharge pressure (subject to a feasibility check against the pump curve).
3. The pressure downstream of PV-03 and FV-02 will be a function of hydraulics as discussed previously. With those conditions understood, the sizings of those valves can be confirmed. There'll be some iteration probably to ensure that the rated valve Cv provides satisfactory operability for the process operating envelope.
4. In my world, the only time I see CFD is for complex hydraulic problems - licence costs limit its use. There is nothing that I'm seeing here that a simple steady state hydraulic calculation couldn't tackle. While long winded, using pencil, paper and a calculator (or a slide rule for those who go back that far) would get the job done to a sufficient tolerance in terms of engineering accuracy. In my opinion, applying CFD here is the metaphorical sledge hammer to crack a nut. I'm pretty sure there is a simple single phase hydraulic spreadsheet in the resources section of this forum that would do just fine.
5. Stream <3> at a velocity of 3.5 m/s is a little bit quick for a greenfield design but is possibly acceptable depending on the situation. However, if the "To Plant" flow stops, then the flow in line <3> will ~double (even if only for a limited time until the issue is recognised - if at all). So, if that happens samin_chemeng, what will happen to the velocity in the line? I'd be checking the ρν² momentum flux against AVIFF (Avoidance of Vibration Induced Fatigue Failure) criteria. In short, design the pipe size to suit the maximum credible flowrate to avoid a piping fatigue failure and potential loss of containment. Fluid flow design economy is a secondary issue but will also benefit from this consideration (this is why velocity criteria still has its place and is an excellent, simple 1st pass screening parameter). Also, don't forget the design calls for A/B pumps so there's a need to consider 2 pumps running, which could also be a cause of more flow.
6. Tie-ing 4 & 5 together to underscore the point. Simple tools can determine a meaningful analysis to guide the design without the need for CFD.

Edited by astro, 06 October 2025 - 07:42 PM.