Converting pressure to flow rate

In summary, the conversation discusses the process of converting differential pressure measurements from a 6-inch diameter pipe into an air flow rate in cfm. The formula for calculating the velocity of the fluid flow is mentioned and the conversation also includes specific calculations and conversions. The individuals involved are trying to determine why their results are higher than expected, but the summary does not provide a solution to this issue.
  • #1
Phobos
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Trying to convert differential pressure (inch WC) measurements from a 6-inch diameter pipe into an air flow rate (cfm).

Here's what I got so far...

I'm assuming laminar, imcompressible flow with negligible friction, head, or thermal losses (this is a very low-flow system). From the Bernoulli equation...

V = (2P/d)^0.5

V = velocity
P = differential pressure
d = air density @ STP

area = A = pi(r^2)

flowrate = Q = VA

Seems straightforward enough, but when I plug in my pressure readings, I'm getting too high of a result for Q (I get a result I'd expect for a fan, and not the dribbling of air I'm actually getting from the pipe).

I think I have the units converted correctly, so am I missing something in the velocity equation?
 
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  • #2
I don't know anything about the topic at hand, but unless you're in 'not even wrong' territory (which it doesn't look like.) You should probably also post your differential pressure, and the flow rate that you got.
 
  • #3
P = 0.001 inch WC (this is the resolution of my meter...which I am taking as the "detection limit"...I've been getting readings higher than that)
r = 3 inches
d = 0.075 pound/cubic foot

results
V = 126.6 ft/min
A = 0.2 ft^2
Q = 24.8 cfm (cubic feet per minute)

I would expect 24 cfm from a fan, not a pipe from which there is no discernable air flow.


or in metric...
P = 0.2486 Pa
r = 0.0762 m
d = 1.202 kg/m3
...
V = 0.643 m/s
A = 0.018 m2
Q = 0.012 m3/s (which converts to the same cfm as above)
 
Last edited:
  • #4
"cfm" is offending your intuition --- translate to linear velocity and watch a smoke marker in the air stream.
 
  • #5
The shorthand I use for this is sqrt(p)*4005=v. So your work checks out. I agree with Bystander - 24.8cfm isn't a whole lot. It is more than "no discernable airflow" though. Its about what a typical 80mm computer case fan gets you on medium power.
 
  • #6
To find the velocity of the fluid flow, multiply the differential pressure by two and divide this number by the density of the flowing material. For example, if the differential pressure is 20 pounds per square inch and the density of the fluid is 80 pounds per cubic foot, the velocity of the fluid is: 2 x (20 psi) / (80 lb/ft3) = 4 feet per second.
 

What is the relationship between pressure and flow rate?

The relationship between pressure and flow rate in fluid dynamics is complex and depends on various factors including the fluid's properties, the geometry of the system, and the type of flow. Generally, an increase in pressure can lead to an increase in flow rate, but the relationship is not always linear.

Can you directly convert pressure to flow rate?

Direct conversion between pressure and flow rate is not straightforward because they are not directly proportional. The flow rate depends not only on the pressure but also on factors like pipe size, fluid viscosity, and the system's overall design.

What is Bernoulli's Equation and how does it relate to this conversion?

Bernoulli's Equation is a principle in fluid dynamics that relates pressure, velocity, and height in a flowing fluid. It can be used to understand how changes in pressure affect the flow rate, especially in systems where the flow is steady and continuous.

How does the type of fluid affect the conversion from pressure to flow rate?

The type of fluid significantly affects this conversion because different fluids have different viscosities and densities. These properties influence how the fluid responds to pressure changes, impacting the flow rate.

Are there any standard formulas to calculate flow rate from pressure?

While there are no universal formulas to calculate flow rate from pressure, specific equations can be used for particular systems. For example, the Hagen-Poiseuille equation can be used for laminar flow in circular pipes, but its applicability is limited to specific conditions.

What tools or devices are used to measure flow rate and pressure in a system?

Flow rate is commonly measured using devices like flow meters, while pressure is measured using pressure gauges or sensors. These instruments provide the necessary data to analyze the relationship between pressure and flow rate in a given system.

How important is pipe diameter in determining the relationship between pressure and flow rate?

Pipe diameter plays a crucial role in determining the relationship between pressure and flow rate. A larger diameter allows for a higher flow rate at the same pressure, due to reduced resistance to the fluid's flow.

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