# Solving an equation with curly brackets and entering into excel

Hi I am sorry if this is a trivial question but I am trying to follow a book to create a mathematical model but I can not get the same result. The equation has curly brackets and I am not sure what it means. If I just treat them as normal parentheses in excel then I get the wrong result. This is driving me crazy any help you can offer would be of great help. The values for each parameter are as follows:

F2 = 0.846 F3 = 2.006 F5 = 0.814 F6 = 0.449

If I enter those into the the corresponding cells in excel (F2-F6) the equation I am entering looks like this:

=F3*((((2*F5*F3)/(F6*EXP(-F3*((1-(F2^2))^0.5))+F5))-F5))

Using this formula I get the answer 5.54 but the book says the answer should be 0.148???? Typically no steps are shown as to how they reached this figure.

I am puzzled as to whether it is something I am doing wrong or whether the book is wrong? I am wondering if am treating the curly brackets wrong or the exp function.

Any help would be much appreciated.

• I plugged the equation into Mathematica and the result for your numerical data was: 5.13427. Could you say a few words about where this is coming from? Maybe the context will help out. – JEM May 4 '14 at 13:05
• These curly brackets are just parentheses. I confirm JEM's result. What I should suggest is to never write a formula like this in a single shot : break it into small pieces to be recombined later. – Claude Leibovici May 4 '14 at 13:39
• It is the solution for a type of solar thermal collector. The values F2-F6 are dimensionless parameters that can be used to give the performance of the collector. The method is outlined in the Solar Engineering of Thermal Process by Duffie and Beckman Edition 2, page 294-296. Does that help? Do you think that there might be a problem with the book then? – alkey May 4 '14 at 13:48
• Yes the ratio FR/F1 = 0.148. It then goes onto say F1 = 6.309 so FR = 6.309 x 0.148 = 0.93 – alkey May 4 '14 at 14:15

## 1 Answer

Thanks everyone for your help. After your suggestions I thought that it must be a problem with the book so I managed to find a newer edition. Sure enough that section had been adjusted. The equation had been replaced with: The parameters needed to solve the equation are:

F2 = 0.846 F3 = 2.006 F5 = 0.814 F6 = 0.449

F4 = 0.63 F1 = 6.31

I entered these into excel using the following:

=F1*F3*F5*(((2*F4)/((F6*EXP(-SQRT(1-((F2^2)))/F3))+F5))-1)

and this gives the correct reading of FR which is 0.93. This means that the ration of FR/F1 is equal to 0.93/6.31 = 0.148.

I still do not know if you can use the equation in my last post to arrive at this result but thank you to everyone for helping.