Fluid mechanics: Pressure and Velocity of gas flow in a heated pipe

In summary: Your Name]In summary, the pressure and velocity of the gas passing through a heated section of pipe will change due to the expansion of the gas as it is heated. However, the exact changes in pressure and velocity cannot be determined without further details about the system. It is important for individuals to continue seeking knowledge and understanding, even outside of school.
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uby
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Homework Statement



Please note this is for my own understanding -- I am no longer in school! I simply cannot find this addressed in introductory texts.

Suppose you have a long pipe of constant cross-sectional area with a heated section in the middle. The system has flowing gas such that the pressure at the inlet (say, 1.1 atm) is slightly higher than the outlet (say, 1 atm).

Assume that the heat transfer rate to the gas is infinitely fast.

As the gas passes through the heated length of pipe, what happens to its pressure and velocity?


Homework Equations


Ideal gas law: PV=nRT
Conservation of mass: flux in = flux out ... (c*b)in = (c*b)out

The Attempt at a Solution


If you draw a control volume with virtual inlet prior to the heated portion of tube and virtual outlet within the heated portion, conservation of mass must be satisfied. So, the convective flux given by concentration*velocity (c*b) should be conserved. Thus, either both variables remain constant or they vary inversely to each other.

From the ideal gas law, the value n/V = concentration = P/RT. Combining with mass conservation:
(P*b/T)in = (P*b/T)out

So, as T changes, so must the product P*b. The open question is ... how do P and b vary? Is it reasonable to assume one is constant? Any ideas?
 
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  • #2


Thank you for your question. It is understandable that you are seeking a better understanding of this concept, even though you are not currently in school. it is important to continually seek knowledge and understanding in various subjects.

Based on the information provided, it seems that the pressure and velocity of the gas will change as it passes through the heated section of the pipe. This is because the gas is being heated, which will cause its volume to expand. This expansion will result in a decrease in pressure, as seen in the ideal gas law equation PV=nRT.

As for the velocity, it will also change as the gas expands and its pressure decreases. This can be seen in the equation of conservation of mass, where the flux in equals the flux out. As the volume of the gas increases, the velocity will decrease in order to maintain the same mass flow rate.

However, it is difficult to determine the exact changes in pressure and velocity without knowing more specific details about the system. It is possible that they both may vary or one may remain constant, depending on the specific conditions of the gas and the heated section of the pipe.

I hope this helps in your understanding. Keep seeking knowledge and never stop learning.


 

1. What is fluid mechanics?

Fluid mechanics is a branch of physics that studies the behavior of fluids (liquids and gases) when they are in motion or at rest. It focuses on understanding the forces and motions of fluids and their effects on surrounding objects.

2. How is pressure defined in fluid mechanics?

Pressure in fluid mechanics is defined as the force per unit area that a fluid exerts on its surroundings. It is typically measured in units of Pascals (Pa) or pounds per square inch (psi).

3. What factors affect the velocity of gas flow in a heated pipe?

The velocity of gas flow in a heated pipe is affected by several factors, including the temperature of the gas, the diameter of the pipe, and the pressure gradient along the pipe. Other factors such as the type of gas and any obstructions in the pipe can also impact the velocity.

4. How does the velocity of gas flow change with temperature in a heated pipe?

As the temperature of a gas increases, its molecules gain more kinetic energy and move faster, leading to an increase in velocity. This is known as the kinetic theory of gases and is one of the fundamental principles of fluid mechanics.

5. What is the significance of studying pressure and velocity of gas flow in a heated pipe?

Understanding the pressure and velocity of gas flow in a heated pipe is important in a variety of fields, such as engineering, environmental science, and meteorology. It allows us to predict and control the behavior of gases in different systems and find ways to optimize their flow for different applications.

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