Isolate equation based on a2: Qa = (Cd*a2)/(sqrt(1 - (a2/a1))) * (sqrt(2*delta-P))/(P)

[MHAutomation]

Hi, I am not able to reverse this equations to isolate a2 on one side.
Could someone help me solve this?

 

[Dr.Peterson]

View attachment 37134

Hi, I am not able to reverse this equations to isolate a2 on one side.
Could someone help me solve this?

I would start by multiplying both sides by the denominator, then squaring. You'll get a quadratic equation, so it won't be a matter of isolating the variable.

You might also find it helpful to temporarily rename chunks of the equation, so it looks something like this: [math]A=\frac{Bx}{\sqrt{1-\frac{x}{y}}}\cdot C[/math] where I've changed [imath]a_2[/imath] to x and [imath]a_1[/imath] to y for ease of writing. Solve for x.

 

[MHAutomation]

Hi Dr. Peterson.

I apoligize for my opening equation. The first picture here is the updated one.

This is the answer i got to, do you agree or disagree?

 

[Dr.Peterson]

Almost. (That little change in the problem does make it a lot easier!)

Where you write Cd, I take it to be a product; is it actually a subscript, C_d?

If so, then I think you're right. (I'd written mine in a slightly different form, so it's hard to compare.)