How Is Absolute Pressure Calculated at Depth in Hydrostatics?

In summary, the absolute pressure at the bottom of a fresh-water lake at a depth of 22.5 m is 322.025 kPa. However, when inputting the answer into webassign, it may be necessary to convert the answer to Pa instead of kPa.
  • #1
kimlu
11
0

Homework Statement



(a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 22.5 m. Assume the density of the water is 1.00x10^3 kg/m3 and the air above is at a pressure of 101.3 kPa.

(b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 33.6 cm?

Homework Equations



P(abs pressure)= ρgh+P(atmospheric pressure)

The Attempt at a Solution



(1000)(9.81)(22.5)+101.3 = 322.025 kPa
I don't understand what I'm doing wrong my webassign says I'm off by a multiple of 10 and I can't do part b without getting part a right :(
 
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  • #2
kimlu said:

Homework Statement



(a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 22.5 m. Assume the density of the water is 1.00x10^3 kg/m3 and the air above is at a pressure of 101.3 kPa.

(b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 33.6 cm?

Homework Equations



P(abs pressure)= ρgh+P(atmospheric pressure)

The Attempt at a Solution



(1000)(9.81)(22.5)+101.3 = 322.025 kPa
I don't understand what I'm doing wrong my webassign says I'm off by a multiple of 10 and I can't do part b without getting part a right :(
This result looks OK to me. 22.5 m of water is on the order of about 60 - 70 ft of water, which is about 2 atm. So your answer, which is a little over 3 atm sounds correct.
 
  • #3
Chestermiller said:
This result looks OK to me. 22.5 m of water is on the order of about 60 - 70 ft of water, which is about 2 atm. So your answer, which is a little over 3 atm sounds correct.

but then why are my calculations wrong according to my webassign answer key :confused:
 
  • #4
kimlu said:
but then why are my calculations wrong according to my webassign answer key :confused:
You do have an error in the working as posted - a factor of 1000 which should have been canceled in converting from Pa to kPa. But as Chet wrote your answer is correct.
When you say the web answer is different by a factor of 10, do you know what that answer is? Is it exactly a factor of 10, or maybe 2308.6 or 123.4? And can you proceed to part b by putting in the web answer?
 
  • #5
haruspex said:
You do have an error in the working as posted - a factor of 1000 which should have been canceled in converting from Pa to kPa. But as Chet wrote your answer is correct.
When you say the web answer is different by a factor of 10, do you know what that answer is? Is it exactly a factor of 10, or maybe 2308.6 or 123.4? And can you proceed to part b by putting in the web answer?

I do not know the correct answer, I only have 5 tries and this is my last try to get it right :frown: and I can proceed to part b whenever I want but for it to be right I need to have the exact right answer for part a so it would help a ton if you could help point out the exact answer which I missed because I still don't quite understand where exactly I went wrong :(
 
  • #6
kimlu said:
I do not know the correct answer, I only have 5 tries and this is my last try to get it right :frown: and I can proceed to part b whenever I want but for it to be right I need to have the exact right answer for part a so it would help a ton if you could help point out the exact answer which I missed because I still don't quite understand where exactly I went wrong :(
Well, here are some possibilities:
1. The answer in webassign is wrong
2. Webassign is looking for the answer in Pa, not kPa
3. Webassign is looking for the answer in atm.

I'm guessing #1.

Chet
 
  • #7
Chestermiller said:
Well, here are some possibilities:
1. The answer in webassign is wrong
2. Webassign is looking for the answer in Pa, not kPa
3. Webassign is looking for the answer in atm.

I'm guessing #1.

Chet

I actually tried putting it in Pa instead and I got it right thank you so much for the tip! :)
 

Related to How Is Absolute Pressure Calculated at Depth in Hydrostatics?

1. What is hydrostatics?

Hydrostatics is the study of fluids at rest, specifically the pressure exerted by a fluid due to its weight.

2. What is absolute pressure?

Absolute pressure is the total pressure at a given point in a fluid, including both the pressure exerted by the fluid's weight and the pressure exerted by the atmosphere above it.

3. How is hydrostatic pressure calculated?

Hydrostatic pressure is calculated by multiplying the density of the fluid by the force of gravity and the depth of the fluid.

4. How does depth affect hydrostatic pressure?

The deeper the fluid, the greater the hydrostatic pressure due to the increased weight of the fluid above it.

5. What is the importance of hydrostatics in everyday life?

Hydrostatics is important in many applications, such as determining the buoyancy of ships and submarines, understanding the behavior of fluids in pipes and containers, and designing structures that can withstand the pressure of water or other fluids.

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