Does anyone have any good tips on deriving equations?

In summary, Joe Ramsey was trying to figure out how speed relates to cross section, and ended up getting frustrated.
  • #1
Joe Ramsey
3
0
I'm very lost !

First off thanks to HallsoIvy and AD for answering my last question. However I am still having a difficult time with the last question.
I know that we are suppose to try these problems before we post…but I am having a horrible time understanding how to derive equations. I am at a loss and I do not know how to even approach this problem. Could someone at least try to get me going?

Here is the question:

A nozzle squirts out a stream of liquid of diameter dnozzle. The nozzle is angled at q above the horizontal. Show that the diameter the stream when it is at its maximum height (dstream) is given by the equation at right (in other words, derive the equation), and therefore does not depend on the rate at which the liquid is coming out of the nozzle, the type of liquid, or anything else.

d_stream= d_nozzel/(square root of cos theta)


Does anyone have any good tips on deriving equations?
 
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  • #2


Originally posted by Joe Ramsey
A nozzle squirts out a stream of liquid of diameter dnozzle. The nozzle is angled at q above the horizontal. Show that the diameter the stream when it is at its maximum height (dstream) is given by the equation at right (in other words, derive the equation), and therefore does not depend on the rate at which the liquid is coming out of the nozzle, the type of liquid, or anything else.

d_stream= d_nozzel/(square root of cos theta)
Along a stream, how does speed relate to cross section? Consider that at any point in the stream, the amount of water flowing per unit time had better be the same. (Otherwise, where's it going?)

Then figure out what the speed of the water is at maximum height compared to its speed at the nozzle.
 
Last edited:
  • #3
Please unsubscribe me from your service.
Thanks,
Joe Ramsey
 
  • #4
I don't think he liked your answer, Doc. :)
 
  • #5
I guess not. :cry:
 

1. How do I derive an equation?

To derive an equation, you need to start with a known equation or set of data and use mathematical principles and logic to manipulate and transform it into a new equation. This process is often done by using calculus and algebraic techniques.

2. What are some tips for deriving equations?

Here are a few tips for deriving equations:

  • Start with the basics: Make sure you have a solid understanding of the fundamental principles and equations related to your topic.
  • Use algebraic manipulation: Use algebraic techniques such as substitution, factoring, and simplification to transform your equation.
  • Apply calculus: Using concepts like derivatives and integrals can help you manipulate equations and find new relationships between variables.
  • Check for consistency: Make sure your derived equation is consistent with known data and principles.
  • Practice: The more you practice deriving equations, the better you will become at it.

3. Can I derive an equation without using calculus?

While calculus is often a useful tool for deriving equations, it is not always necessary. You can use algebraic techniques and logical reasoning to derive equations without relying on calculus. However, calculus can make the process more efficient and help you find relationships between variables that may not be immediately apparent.

4. Is there a specific order to follow when deriving equations?

There is no specific order that you must follow when deriving equations. However, it is generally helpful to start with the basics and build upon them, rather than trying to derive a complex equation without a solid understanding of the underlying principles. It can also be helpful to break down the problem into smaller parts and tackle them one at a time.

5. How do I know if my derived equation is correct?

To ensure the accuracy of your derived equation, you can check for consistency with known data and principles. This means plugging in values for the variables and seeing if the equation holds true. You can also double-check your steps and calculations to make sure they are accurate. In some cases, it may also be helpful to have someone else review your work for any errors or oversights.

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