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goldfish9776
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Homework Statement
i couldn't understand why the pressure P1 is given by P atm - ρ water (gh2) - ρ(oil)(gh1) + ρ(mercury)(gh3) .Where is the point P1 ? It's not indicated in the diagram ...
isn't the air pressure at water surface = atmospheric pressure , which is 85.6Pa ?gneill said:It looks like P1 is meant to be the pressure at the water/air interface in the tank. So, it's the same as the air pressure in the tank.
Nope. That would be the pressure at the open end of the "S" tube.goldfish9776 said:isn't the air pressure at water surface = atmospheric pressure , which is 85.6Pa ?
ok , can you explain why the pressure at P1 is found by subtracting the ρ water (gh2) and ρ(oil)(gh1) and plus ρ(mercury)(gh3) ??gneill said:Nope. That would be the pressure at the open end of the "S" tube.
The tank is a sealed enclosure except for the tube, and the enclosed air can have a different pressure than atmospheric.
I think you are right. I hadn't written out and simplified the full path equation before, now I have and I agree with you. Thanks for catching that.Chestermiller said:If looks to me like they have the h2 and the h1 incorrectly switched in the equation.
Chet
so P1 = Patm +ρ (water)gh2 - ρ(oil)g(h1+h2) + ρ(oil)gh1 - ρ(water)g(h1+h2) + ρ(mercury)gh3gneill said:I think you are right. I hadn't written out and simplified the full path equation before, now I have and I agree with you. Thanks for catching that.
I've modified the diagram in my previous post to reflect the full path. Points with the same letter labels are at the same pressure. The OP should be able to follow the path summing the pressure changes, then simplify the result.
Yes. That's correct.goldfish9776 said:so P1 = Patm +ρ (water)gh2 - ρ(oil)g(h1+h2) + ρ(oil)gh1 - ρ(water)g(h1+h2) + ρ(mercury)gh3
P1 = Patm - ρ(water)gh1 - ρ(oil)gh2 + ρ(mercury)gh3 ?
The purpose of solving a pressure puzzle is to determine the value of pressure (P1) in a system, based on given information and equations related to pressure and fluid mechanics.
First, carefully analyze the given diagram and identify all known values and variables. Then, use equations such as Pascal's Law and the continuity equation to set up a system of equations. Finally, solve for the unknown pressure (P1) using algebraic manipulation.
Finding P1 is significant because it allows us to understand the behavior of fluids in a system and make predictions about how pressure will change in different parts of the system.
Some common mistakes to avoid when solving a pressure puzzle include using incorrect equations, incorrectly identifying known values and variables, and making errors in algebraic manipulation. It is important to double-check your work and carefully follow each step in the solving process.
Yes, a pressure puzzle can have more than one solution. This is because there may be multiple ways to set up the equations and solve for P1. However, it is important to check the validity of each solution and choose the most reasonable and physically sound answer.