Small pipe break for an ideal gas

Click For Summary
SUMMARY

The discussion centers on calculating the flow rate of an ideal gas escaping through a small break in a large tube, where the initial pressure (p1) is significantly higher than the external pressure (p2). The process is identified as adiabatic and isentropic, leading to the conclusion that the change in enthalpy and kinetic energy must balance. Key equations referenced include the ideal gas law (pv = rT) and a modified Bernoulli equation for compressible flow. Participants emphasize the importance of knowing the size of the break and the nature of the gas expansion (isothermal vs. adiabatic) to accurately determine flow characteristics.

PREREQUISITES
  • Understanding of ideal gas laws, specifically pv = rT
  • Familiarity with adiabatic and isentropic processes in thermodynamics
  • Knowledge of compressible flow dynamics and the Bernoulli equation
  • Basic calculus for handling differential equations in fluid dynamics
NEXT STEPS
  • Study the compressible flow version of the Bernoulli equation
  • Learn about adiabatic and isothermal expansion processes in gases
  • Research flow rate calculations for small openings in pressurized systems
  • Explore the implications of density variations in compressible fluid flow
USEFUL FOR

This discussion is beneficial for students and professionals in mechanical engineering, particularly those focusing on fluid dynamics, thermodynamics, and gas flow analysis. It is also relevant for anyone involved in designing systems with pressurized gases.

eXorikos
Messages
281
Reaction score
5

Homework Statement


A large tube filled with an ideal gas at pressure p1 and temperature T1 has a small break in it towards an envirronement at p2, with p1 much larger than p2. What is the flow rate through the hole to the outside of the tube.

Homework Equations


pv=rT
Δh+Δc2/2=δq-δl
h1 + c12 = h2 + c22/2

The Attempt at a Solution


The proces is adiabatic and isentropic so Δh+Δc2/2=0
Since it is a large tube it can be presumed that c1=0. Since p2 is much lower than p1 we can presume h2 = 0.

Am I on the right track here?
 
Physics news on Phys.org
Is this the exact wording of the problem statement?
 
Yes. Do you need size of the break?
 
eXorikos said:
Yes. Do you need size of the break?
Sure. If the size of the break is zero, then the flow rate is zero.
 
Since the whole exercise is symbolic, let's assume size A which is small. Than the equation I mentioned would give the velocity, we have A and I can find the density using the total state of the system.

Is this correct?
 
eXorikos said:
Since the whole exercise is symbolic, let's assume size A which is small. Than the equation I mentioned would give the velocity, we have A and I can find the density using the total state of the system.

Is this correct?
What makes you think that h2 can be taken as zero? Are you familiar with the compressible flow version of the Bernoulli equation? Do you think that the gas in the tank approaching the exit hole will be experiencing something close to (a) isothermal expansion or (b) adiabatic expansion? Do you think that the gas flow will be close to reversible expansion or no?
 
Good points. Than I have no idea on how to approach this problem.

Can you point me into a direction?
 
My leading questions were to get you pointed in the right direction. Here's another hint: for the flow approaching the exit hole in the tank,
$$dh=-vdv$$
 

Similar threads

  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 3 ·
Replies
3
Views
5K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
9K
  • · Replies 1 ·
Replies
1
Views
5K
  • · Replies 12 ·
Replies
12
Views
2K
Replies
3
Views
2K