Flow Rate, Velocity and Pressure relationship

[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.

 

[Chestermiller]

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

 

[smithson1984]

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

 

[Chestermiller]

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