Mass loss in Bernoulli's Principle?

In summary, the conversation discusses the effect of losing mass on the velocity of a freestream air traveling down a tube. It is determined that if the flow is slow enough, the air would slow down to 1m/s due to the continuity principle. This principle is illustrated in the example of duct systems for ventilation or air conditioning.
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udtsith12
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Hi, I could really use help. I am trying to understand what would happen to the velocity of a freestream air if it loses mass while traveling down a tube. For example, suppose that you have 1 cubic meter of air traveling at 10 m/s down a duct with a 1m^2 cross section. And then suppose that you lose via pumps along the tube 90% of the air. Or another way to say it... suppose that 90% of the air just disappeared as it was traveling down the pipe. What would be the resulting velocity of the remaining air? My closest guess is that it would be reduced to 1 m/s. Is that right? Thanks!
 
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  • #2
Assuming that your flow is slow enough to consider incompressible, then yes, simple continuity would indicate that it would slow down to 1m/s. This isn't due to Bernoulli, it's just the continuity principle.
 
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Likes gmax137
  • #3
Welcome, udtsith12 :cool:

If you observe a duct system for ventilation or air conditioning, you could see that the area of the cross-section is reduced (for supply ducts) or increased (for return ducts) gradually as the flow advances downstream, more or less after one or two air diffusers or grilles.

Those changes of cross-section have the purposse of avoiding as much as possible changes of the velocity of the airstream as it loses mass while traveling down the duct.

hvac.jpg
 

1. What is Bernoulli's Principle?

Bernoulli's Principle is a fundamental concept in fluid dynamics that states that as the velocity of a fluid increases, the pressure exerted by that fluid decreases. This principle is based on the conservation of energy and is commonly observed in everyday phenomena such as the lift force on an airplane wing or the flow of water through a narrow pipe.

2. How does Bernoulli's Principle relate to mass loss?

Bernoulli's Principle does not directly relate to mass loss. However, it can be applied to understand the decrease in pressure and increase in velocity that occurs when a fluid flows through a constriction, such as in a venturi tube. This can result in a decrease in mass flow rate, but the total mass of the fluid remains constant.

3. What factors can affect mass loss in Bernoulli's Principle?

The mass loss in Bernoulli's Principle is affected by the velocity of the fluid, the density of the fluid, and the size and shape of the constriction. Other factors such as the viscosity of the fluid and the presence of turbulence can also play a role.

4. Can mass loss occur in other applications of Bernoulli's Principle?

Yes, mass loss can occur in other applications of Bernoulli's Principle. For example, in a carburetor, the decrease in pressure caused by the constriction results in a decrease in mass flow rate of fuel into the engine. This principle is also used in atomizers, where a high-velocity fluid stream is used to break up a liquid into small droplets, resulting in a decrease in mass of the liquid.

5. Are there any practical applications of mass loss in Bernoulli's Principle?

Yes, there are several practical applications of mass loss in Bernoulli's Principle. One example is in the design of sprinkler systems, where the decrease in pressure caused by the constriction in the sprinkler head results in a decrease in water flow rate. This allows for more efficient use of water while still providing adequate coverage. Another example is in the design of carburetors and atomizers, as mentioned previously.

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