How to find force from volumetric flow rate and pressure

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SUMMARY

This discussion focuses on calculating thrust force (Fthrust) from volumetric flow rate (Q) and pressure (P) in the context of designing a remote-controlled hovercraft. The key equations involved are Q = velocity * Area and F = mass * acceleration. The participant identified a slope of -0.285 [m3/s/mmH20] and is attempting to determine the y-intercept (F0) and the constant γ, which represents the slope of the thrust versus velocity relationship. The discussion emphasizes the importance of understanding how pressure influences force and flow rate in fan systems.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly the relationship between pressure and force.
  • Familiarity with the equations of motion, specifically F = mass * acceleration.
  • Knowledge of volumetric flow rate calculations, including Q = velocity * Area.
  • Basic graph interpretation skills to analyze pressure versus flow relationships.
NEXT STEPS
  • Research the relationship between pressure and force in fluid dynamics.
  • Learn how to derive thrust equations for fan systems in hovercraft design.
  • Explore methods for approximating linear relationships in experimental data.
  • Study the implications of atmospheric pressure on fan performance and thrust generation.
USEFUL FOR

Engineers, physics students, and hobbyists involved in hovercraft design or fluid dynamics who seek to understand the relationship between volumetric flow rate, pressure, and thrust force.

bl965
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1. Homework Statement
Hi. This is a problem related to designing a RC hover craft. We are given a datasheet for a fan used as thrust.
http://imgur.com/6liZSid Sorry image post no working, url: http://imgur.com/a/6XLwL
We have to approximate the equation to a straight line through the curve. Then relate it to Fthrust = F0+ γ*v. We have to find γ and what F0 represents.

Homework Equations


Q = velocity * Area
F = mass * acceleration

The Attempt at a Solution


I found that the slope is -0.285 [m3/s/mmH20]. To find F0, I think the graph has to be turned on its side: pressure is the independent variable and volumetric flow is the dependent. If pressure is zero, I can find F0 which is the y intercept. But how to relate force to volumetric flow or velocity.
 
Last edited:
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If P is the pressure and A is the area that the pressure acts on, what is the force?
 
If pressure is 0, volumetric flow is high, and small pressure * area is small force. As pressure increases, there will be more force with less flow. Makes sense. From start the fan is operating at atmosphere. I get high results when I search for one atmosphere in mm of water. Am I on the right track?
 
bl965 said:
If pressure is 0, volumetric flow is high, and small pressure * area is small force. As pressure increases, there will be more force with less flow. Makes sense. From start the fan is operating at atmosphere. I get high results when I search for one atmosphere in mm of water. Am I on the right track?
I have no idea. Can you please provide an exact problem statement?
 
(b) We can relate this linear relationship to Fthrust = F0-γv [Note: γ is a constant representing the slope of the F(v) line]. For each fan, based on your approximation in (a), what are the values for F0 and for γ?
 
bl965 said:
I think the graph has to be turned on its side:
No, it looks the right way around already, with pressure on the vertical axis. Seems to me you flipped it around in order to get:
bl965 said:
I found that the slope is -0.285 [m3/s/mmH20].

bl965 said:
how to relate force to volumetric flow or velocity.
What do you think relates volumetric flow through an aperture to the linear flow rate through it?
As Chester asks, what relates pressure to force?
 

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