# Flow Rate in Pipe: Q, v, A Explained

That's why the Piping and Instrumentation Diagram (P&ID) has pressure drop lines as a central element.In summary, the flow rate in a pipe is determined by the velocity of the fluid and the inner area of the pipe, according to the general rule Q = v * A. However, this formula does not take into account factors such as pressure loss and friction in the pipe. The pump providing the flow rate may be limited by its power and may succumb to accumulating friction losses, causing a decline in flow rate. To fully understand the relationship between friction losses, power, and flow rate, additional equations such as Bernoulli's equation and the viscosity of the fluid must be considered. In designing a fluid duct or

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!

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
Good understanding.
unlimited power then the flow rate would remain the same right ?
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?

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

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.

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.

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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.

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

Chet

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.

## 1. What is flow rate in a pipe?

Flow rate in a pipe refers to the volume of fluid that passes through a given point in the pipe per unit time. It is typically measured in units of volume per time, such as gallons per minute or cubic meters per second.

## 2. What is the difference between Q, v, and A in flow rate?

Q, v, and A are all related to flow rate in a pipe, but they represent different variables. Q represents the volumetric flow rate, or the volume of fluid passing through a given point in the pipe per unit time. v represents the velocity of the fluid, or the speed at which the fluid is moving through the pipe. A represents the cross-sectional area of the pipe, which is used to calculate the volumetric flow rate.

## 3. How is flow rate calculated in a pipe?

Flow rate in a pipe can be calculated using the equation Q = vA, where Q is the volumetric flow rate, v is the velocity of the fluid, and A is the cross-sectional area of the pipe. This equation takes into account the relationship between velocity and cross-sectional area, as well as the time component of flow rate.

## 4. How does the diameter of a pipe affect flow rate?

The diameter of a pipe plays a significant role in flow rate. As the diameter of a pipe increases, the cross-sectional area also increases, resulting in a larger flow rate for the same velocity. This means that a larger pipe can transport more fluid than a smaller pipe in the same amount of time.

## 5. What factors can affect flow rate in a pipe?

Several factors can affect flow rate in a pipe, including the diameter of the pipe, the viscosity of the fluid, the roughness of the pipe's interior surface, and the pressure gradient along the pipe. Changes in any of these factors can alter the flow rate and should be considered when designing or analyzing a pipe system.