Help in rearranging a formulae

[Fornicis]

Hi all,

I was wondering if anyone could give me a hand in rearranging the following formulae to make v the subject?

PAvail = 1/2 ρAv$^{3}$C$_{p}$

This isn't for homework, its simply something I'm interested in and I would be immensely grateful to anyone who could do this for me.

Oh and before anyone says, I have tried to myself but I just want a second opinion as what it came out with for me seemed a bit off

 

[tfr000]

v³ = (2PAvail) / (ρAC_p)
and then take the cube root of both sides.

Is "PAvail" five different variables, or two, or one? Hard to tell... Anyway, same answer in any case.

 

[Fornicis]

Thats similar to what I got, though less brackets which could have resulted in miscalculations, and in this case its just one but as you said, it can be interchangeable, and that part is key :) thank you very much

 

[Mark44]

Hi all,

I was wondering if anyone could give me a hand in rearranging the following formulae to make v the subject?

PAvail = 1/2 ρAv$^{3}$C$_{p}$

Minor point: this is a formula. Formulae is the plural of formula.

This isn't for homework, its simply something I'm interested in and I would be immensely grateful to anyone who could do this for me.

Oh and before anyone says, I have tried to myself but I just want a second opinion as what it came out with for me seemed a bit off

 

[CellCoree]

.

Sure, I'd be happy to help you rearrange the formula to make v the subject. Here's how we can do it:

First, let's multiply both sides of the equation by 2 to get rid of the 1/2 on the right side:

2PAvail = ρAv^{3}C_{p}

Next, we can divide both sides by ρA to isolate the v^3 term on the right side:

(2PAvail)/(ρA) = v^{3}C_{p}

Now, we can take the cube root of both sides to get v by itself:

v = (2PAvail/(ρA*C_{p}))^{1/3}

And there you have it! v is now the subject of the formula. I hope this helps and let me know if you have any further questions. Happy to assist!