Regression rate of fuel in rocket nozzle

  • Thread starter TimeRip496
  • Start date
254
5
upload_2017-12-14_12-52-45.png

So we have: stability for n < 1
instability for n > 1
upload_2017-12-14_12-53-43.png


I assume to get the time growth, I have to integrate the above first eqn. However I also get ln(δpc) at the LHS from the integrating. However the above equation for time growth removed that ln(δpc) and thus I can't seem to get past this part.

Source: https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-50-introduction-to-propulsion-systems-spring-2012/lecture-notes/MIT16_50S12_lec9.pdf
 

Attachments

560
88
When ##\frac{1}{y}\frac{dy}{dt}=-C## then integrating both sides leads to ## \ln(y) = -Ct ## (neglecting the constant of integration)
Taking the exponential of the left side leads to ## \exp(\ln(y)) = e^{\ln(y)} = y ##
Taking the exponential of both sides leads to ##y = \exp(-Ct) =\frac{1}{e^{Ct}}##
hope this helps.
 
254
5
When ##\frac{1}{y}\frac{dy}{dt}=-C## then integrating both sides leads to ## \ln(y) = -Ct ## (neglecting the constant of integration)
Taking the exponential of the left side leads to ## \exp(\ln(y)) = e^{\ln(y)} = y ##
Taking the exponential of both sides leads to ##y = \exp(-Ct) =\frac{1}{e^{Ct}}##
hope this helps.
Thanks I get this part. However the one shown on the pdf does not have the exponential for the time growth equation. How did they arrive at the above equation while getting rid of the exponential?
 
560
88
well, how much time does it take for ##y## to change from ##y_0## at ##t=0## to say ##2y_0##?

at ##t=0## we have ##y=\exp(0) = 1 ##, so ##y_0=1##
and at time t, we have from the equation ##\ln(y) = Ct## (I make it positive here because your equation has a negative constant):
##t = \frac{1}{C} \cdot \ln(2) ##

so to double ##y##, it takes ##t = \frac{1}{C} \cdot \ln(2) ## seconds, with a scaling factor for doubling (or tripling or whatever) of ## \frac{1}{C}##

hope this helps...
 

Want to reply to this thread?

"Regression rate of fuel in rocket nozzle" You must log in or register to reply here.

Related Threads for: Regression rate of fuel in rocket nozzle

  • Posted
Replies
6
Views
3K
Replies
14
Views
3K
  • Posted
Replies
7
Views
9K
  • Posted
Replies
8
Views
4K
  • Posted
Replies
11
Views
4K
Replies
6
Views
767
Replies
2
Views
2K
Replies
3
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top