Can One Pressure Sensor Accurately Measure Flow Rate in a Pipe System?

[Sangwookim]

Hello,

I am stuck on a pipe flow measurement problem and I would love if some excellent minds would help me out.
I have a robot that sprays paint, and there is a motor pump providing the paint to it. I need to be able to measure the flow rate (velocity) of the paint going through the nozzle.
Would someone be able to give me a very elegant and simple way to theoretically explain why I can't use one pressure sensor to get flow rate?
I know that Bernoulli's principle relies on a pressure difference, and that there doesn't exist a commercial solution that measures flow rate with just one sensor.
But what about these points that seems to counter the above?
- If I have a vacuum cleaner, and there is a hole in the side of the tube, I can feel the air blowing into that hole. If I were to increase the motor speed of the vacuum, then this air blowing into the side hole is increased. If I were to put just one pressure sensor in that hole, wouldn't I get a correlation between that reading and the flow rate of the air? What am I missing in this analogy?
- If we need a pressure difference to get the flow rate, why can't I just use the outside air (that we are spraying into) as the other pressure value? Since it is about 0 psi environment that we are spraying to, can't we use that as the other pressure value, thereby calculating flow?
- I know that if we close the nozzle valve and run the pump, then the sensor would sense increased pressure while speed remains at zero, giving us a faulty value. But what if we just choose to measure the pressure only when we know the valve is open? Could we get a correlation between the one pressure reading and flow?

The problem is, I intuitively know that it isn't possible to use just one pressure sensor. I know I need two, but I can't come up with a really elegant theoretical explanation/analogy to really convince myself. I also need to disprove the above counterpoints to really convince myself. Your wisdom and knowledge is greatly appreciated!

Sangwoo

 

[Achy47]

Hello Sangwoo,

Thank you for reaching out for help with your pipe flow measurement problem. I understand the importance of finding a theoretical explanation for a problem before trying to solve it practically. Let me try to provide you with a simple and elegant explanation for why one pressure sensor is not enough to accurately measure flow rate in your paint spraying system.

First, let's consider your analogy of the vacuum cleaner with a hole in the side of the tube. While it is true that increasing the motor speed of the vacuum will increase the air blowing into the hole, this does not necessarily mean that the flow rate has increased. The pressure sensor in this case is only measuring the pressure at that specific point in the tube, and it does not take into account the overall flow rate of the system. In other words, the pressure at that point may increase due to the increased motor speed, but this does not necessarily mean that the overall flow rate has increased as well. There could be other factors, such as obstructions or changes in the diameter of the tube, that affect the overall flow rate but may not be reflected in the pressure sensor reading at that specific point. Therefore, using just one pressure sensor in this case would not give an accurate measurement of the flow rate.

Next, let's consider your suggestion of using the outside air as the other pressure value. While it is true that the outside air is at 0 psi, it is not a constant value. The outside air pressure can change depending on external factors, such as wind or altitude, which would affect the accuracy of your flow rate measurement. Additionally, using the outside air pressure as a reference point would not take into account any changes in pressure within the system itself. For example, if there is a blockage or constriction in the nozzle, the pressure within the system would increase and the outside air pressure would not accurately reflect this change. Therefore, two pressure sensors are necessary to accurately measure the flow rate in this case.

Finally, let's address your concern about measuring the pressure only when the valve is open. While this may seem like a possible solution, it would not give an accurate measurement of the flow rate. As you mentioned, when the valve is closed, the pressure would increase while the speed remains at zero, leading to a faulty reading. However, even when the valve is open, there can still be fluctuations in pressure within the system that would not be captured by just one pressure sensor. This is why two