Confused about the pressure formula

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The discussion centers on two pressure formulas: p = p0 + rho*g*h and p = rho*g*d. The first formula accounts for the initial pressure, typically atmospheric pressure, while the second calculates only the pressure exerted by the fluid. The need for atmospheric pressure inclusion depends on whether the total pressure or just the fluid pressure is required. For a research submarine's maximum safe depth, the choice of formula hinges on whether the inward force from the water or the net inward force is considered. Ultimately, the recommendation leans towards using the formula without atmospheric pressure for calculations in this context.
jayadds
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Hi,

I've come across two different formulae for pressure:

p = p0 + rho*g*h (p0 = initial pressure)

OR

p = rho*g*d

My question is, why does one of the formulae includes the initial pressure (initial pressure is often the atmospheric pressure = 1.013*10^5 Pa) in the formula whereas the other one doesn't? Do they actual calculate the same thing?

Many thanks.
 
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The second version just gives the pressure due to the fluid (density rho). If you want the full pressure, you need to add the pressure above the fluid, p0.
 
Doc Al said:
The second version just gives the pressure due to the fluid (density rho). If you want the full pressure, you need to add the pressure above the fluid, p0.

Having said that, then for the following question should I use the formula with or without the atmospheric pressure?

A research submarine has a 20 cm diameter window. It can withstand forces up to 1.0 x 10^6 N. What is the submarine's maxiumum safe depth in water?
 
Depends. Do they mean the inward force from the water or the net inward force? (Presumably, the pressure inside the submarine is atmospheric.) Lacking additional information, I would use the one without the atmospheric pressure.
 
Personally, I'd use the 'pessimistic' version. But I may be just a wimp.
 

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