×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Maths question RE summation symbol

Maths question RE summation symbol

Maths question RE summation symbol

(OP)
Hi everyone,

I'm integrating a PV diagram. I have successfully done the integration, but now just want to show that the final value is the sum of all the values collected for each crank angle, from let's say for instance 1 degree to 180 degrees.

I could just not bother using the symbol and just explain in words, but I'd like to know how to properly use the summation symbol. The image below is my guess at how I could use it in this situation. Please tell me if this is incorrect ! Thanks

RE: Maths question RE summation symbol

whew, it has been a long time... but based on what you've written I gather that:
1) you've not done the integral, you've done a step-by-step summation of values by crank angle
2) you want to show THAT in equation form

My proposal is that you want Sum(theta from 1 to 180)[P(theta)*(V(theta)-V(theta-1)]

RE: Maths question RE summation symbol

(otherwise you're talking about the finite integral from vmin to vmax of P, and no summation sign is needed?)

RE: Maths question RE summation symbol

(OP)
I've done a trapezoidal numerical integration of the pressure and volume data I have, for crank angles in 0.5 degree increments.

The image below is a screenshot of the spreadsheet:


RE: Maths question RE summation symbol

(OP)
So for instance I wanted to find the work done per unit volume from cells A5 to A8. I would sum cells D5:D8 and divide by the cylinder's total displacement volume. I wish to show this as an equation using the summation symbol

RE: Maths question RE summation symbol

It is wrong as you've used a summation and an integral sign, which indicates a double summation.

So, lose the algebraic integral sign, and add a subscript theta to the P. Change the d to a small delta.

So it should be

sigma super 180 sub theta=0 P sub theta dot small_delta V



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Maths question RE summation symbol

(OP)
Many thanks for your help. Is this now correct?

RE: Maths question RE summation symbol

I you are attempting to show an integration, then it should be a definite integral, so, the integral symbol with limits, rather than summation. The summation is the mathematical approach to solving for the integral in question.

TTFN
FAQ731-376: Eng-Tips.com Forum Policies

RE: Maths question RE summation symbol

the more recent summation was closer, but deltaV is dependent on theta and should show it. That's why I suggested (1 to 180) and (Vtheta-Vtheta-1)

RE: Maths question RE summation symbol

You may also find that since P and V both vary during the time-step that a more appropriate value for dVtheta might be required so that the approximated dV is closer to the measured value of P. Something like (Vtheta+1 -Vttheta-1).




- Steve

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources