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Isolating quantities — Basic example

Video transcript

the absolute pressure P in a fluid of density Rho I know this looks like a lowercase P but this is the Greek letter Rho which we typically use for density at a given depth H can be found with the above equation where capital P with a little subscript of this I guess P Sub Zero or may be interested in oh it looks like a zero P Sub Zero is atmospheric pressure and G is gravitational acceleration which of the following is the correct expression for the depth in terms of the absolute pressure atmospheric pressure fluid density and gravitational acceleration so essentially what we want to do is we want to solve for depth we want to solve for we want to solve for H so let's see if we can do that so we have P is equal to P sub I'll call this P Sub Zero plus Rho times G times H now to solve for H I at least want to isolate this term that contains H on the right hand side and so let me subtract P Sub Zero from both sides so subtract P Sub Zero subtract P Sub Zero and then on the left hand side I have capital P minus P capital P sub 0 is equal to those are going to cancel out you're gonna have Rho times G times H and now to solve for H I can divide both sides by Rho times G so let's do that let's divide this side time by Rho times G and let's divide this side by Rho times Rho times G Rho times G divided by Rho times G is just going to be 1 and we get H is equal to this thing right over here we could say H is equal to capital P minus capital P Sub Zero over Rho times G and that is the first choice right over there