Flow Rate, Velocity and Pressure relationship

• smithson1984
In summary: I don't think so. I think that the dominant effects are going to be frictional pressure drop and possibly potential energy change.
smithson1984
Hello everyone,

I'm new to this forum and this is my first post so go easy!

I have an engineering problem which I am uncertain as to how to solve. I am trying to design a basic ballast system for pumping seawater. The idea is to use compressed air to evacuate the water through a series of pipes. By controlling the compressed air the pressure will be known at "inlet". So the following information is known:

Inlet

- Pressure = 6 bar
- Flow Rate = 0.783 l/s

Outlet

- Pressure = 1 bar
- Flow Rate = 0.783 l/s
- Pipe Diameter = D

What I desire to know is what diameter pipe I will require at outlet to permit the above flow rate. I realize the answer may not be simple but any suggestions of which approaches or formulas would be much appreciated!

I have tried using Bernoulli's equation which hasn't come back with sensible results. One of the problems is that the Inlet surface area is unknown (and constantly changing).

Thanks in advance for any input!

Ian

PS, I have attached an image to explain a little further.

Attachments

• pressure, Flow Rate and Velocity.jpg
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You need to take into account the frictional pressure drop (turbulent viscous) in the piping network. To do this, you need the pressure drop - flow rate relationship for a fluid thorough a straight section of pipe, and you need to include additional pressure drop for elbows and bends. See Bird, Stewart, and Lightfoot, Transport Phenomena.

Chet

Chestermiller said:
You need to take into account the frictional pressure drop (turbulent viscous) in the piping network. To do this, you need the pressure drop - flow rate relationship for a fluid thorough a straight section of pipe, and you need to include additional pressure drop for elbows and bends. See Bird, Stewart, and Lightfoot, Transport Phenomena.

Chet
Thanks for the reply Chet. It's much appreciated! I will make sure to seek out the book you advised.

Do you think the Bernoulli approach would be sufficient for a first approximation in the case of this system? I am a bit confused as I am unsure whether it can be;

a) considered a continuous system (and hence use the continuity equation) because of the presence of a free surface.
b) the inlet velocity can be considered zero (hence no dynamic pressure) as it is relatively much slower in comparison to outlet

Thanks again for any response,

Ian

smithson1984 said:
Thanks for the reply Chet. It's much appreciated! I will make sure to seek out the book you advised.

Do you think the Bernoulli approach would be sufficient for a first approximation in the case of this system? I am a bit confused as I am unsure whether it can be;

I don't think so. I think that the dominant effects are going to be frictional pressure drop and possibly potential energy change.
a) considered a continuous system (and hence use the continuity equation) because of the presence of a free surface.
This won't be a major issue. Just treat the flow as quasi steady state.
b) the inlet velocity can be considered zero (hence no dynamic pressure) as it is relatively much slower in comparison to outlet
As I said above, the outlet velocity effect is probably going to be negligible too.

Chet

1. What is the difference between flow rate and velocity?

Flow rate refers to the volume of fluid passing through a given point in a specific amount of time, typically measured in liters per second. Velocity, on the other hand, is the speed at which the fluid is flowing, typically measured in meters per second.

2. How are flow rate, velocity, and pressure related?

In a closed system, flow rate, velocity, and pressure are all interdependent. An increase in flow rate will result in an increase in velocity, which in turn can cause a decrease in pressure due to Bernoulli's principle. Similarly, a decrease in flow rate can lead to a decrease in velocity and an increase in pressure.

3. Does the size of a pipe affect flow rate and velocity?

Yes, the size of a pipe can greatly impact flow rate and velocity. A larger pipe will allow for a greater volume of fluid to pass through, resulting in a higher flow rate and potentially lower velocity. A smaller pipe will have the opposite effect, with a lower flow rate and higher velocity.

4. How does fluid viscosity affect flow rate and velocity?

Viscosity, or the resistance of a fluid to flow, can greatly impact flow rate and velocity. A more viscous fluid will have a lower flow rate and velocity compared to a less viscous fluid. This is because the more viscous fluid experiences more internal friction, resulting in a slower flow.

5. Can flow rate, velocity, and pressure be controlled?

Yes, flow rate, velocity, and pressure can be controlled through various means such as adjusting the size of the pipe, changing the pump speed, or using valves and regulators. These adjustments can help maintain a desired flow rate, velocity, and pressure in a system.

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