# Flow rate in a pipe

1. Jan 20, 2015

Hi,

I have a question regarding the flow rate in a pipe. According to the general rule the flow rate is:

Q = v * A

where Q [m3/s]
v [m/s]
A [m2]

So according to this formula the flow rate depends only on the inner area of the pipe and the velocity of the fluid and does not matter what the pressure loss is until a certain point. So I had this argument this other day with someone and he said that the flow rate depends on the friction losses in the pipe. But I don't see where that happens according to this formula. If I have a pump that provides 2 [m3/h] and there is only one pipe, no matter how long or how many curves it makes the water flow at the end of the pipe will still be 2 [m3/h] because no mass is lost anywhere if there is no ramification.
The only doubt that I have is that the pump might not be able to provide 2 [m3/h] because it has limited power therefore it will soon succumb to the accumulating friction losses in the pipe therefore the declining flow rate. But if the pump would have unlimited power then the flow rate would remain the same right ? Anyway I could not find the relation between the friction losses, power and flow rate and how this all comes together in an elegant explanaition and if someone could provide one it would be much appreciated. Thanks!

2. Jan 20, 2015

### Bystander

Good understanding.
Another good understanding.
For an incompressible fluid flow rate through a straight tube of constant radius (diameter) is given by

(dV/dt) = (πr4ΔP)/(8ηL), where "r" is the radius of the tube/pipe, "L" is the length, "ΔP" is the difference in pressure between inlet and outlet of the tube, and "η" is the viscosity of the fluid.

Do you want to go into more detail?

3. Jan 20, 2015

### Staff: Mentor

To expand on what Bystander said, if you fix the volume flow rate (and the fluid is incompressible), the pressure drop in the pipe will adjust itself to conform to this.

Chet

4. Jan 21, 2015

### Staff: Mentor

Just a comment on the root cause of the issue: this is a matter of not understanding how equations apply to the real world (a common issue). An equation means what it says and nothing more. If it doesn't include pressure, that does NOT mean pressure is irrelevant in all cases involving flow, it just means that the person who wrote the equation decided to focus on describing something else. The equation relates three quantities and IF you know two you can find the third, but it doesn't say where you got them.

Consider two types of flow meters:
A turbine flow meter measures flow velocity using a spinning paddle wheel. So you need only the pipe diameter and that equation to find the flow rate.

A pito array measures pressure, so you need Bernoulli's equation to find the velocity, THEN you can use Q=VA to find flow rate.

So yes, pressure definitely matters for fluid flow, but whether it enters a particular problem depends on the problem.

5. Jan 21, 2015

Thanks for your answers, I guess the flow rate does in fact depend on more than just flow area and velocity... I'm guessing that the formula above can be applied directly only for ideal cases, no friction with pipe, between particles etc., otherwise I need to find the flow by other means.

Last edited: Jan 21, 2015
6. Jan 21, 2015

### Bystander

Hey, you did fine understanding that mass had to be conserved between the inlet and outlet of the pipe, and understanding that the longer the pipe, the harder the pump has to work to maintain flow rate. The rest of the bookkeeping on flow problems is NOT so obvious.

7. Jan 21, 2015

### Staff: Mentor

That's not what I said, and it applies much more widely than just ideal cases.

Chet

8. Jan 21, 2015

### Staff: Mentor

Right: Q=VA is a very small piece of a much larger problem. When designing a fluid duct/piping system, pressure drop/rise plays a critical role.