Pressure Problem (math error I think)

In summary, at a point in the ocean about 9.60 km deep, the pressure is huge, about 9.89 x 10^7 N/m^2. Under these conditions, the volume of water will decrease by .034 m^3.
  • #1
esinn08
8
0
Hi everyone,

My question is as follows:

Consider a point in the ocean about 9.60 km deep. The pressure at that point is huge, about 9.89 x 10^7 N/m^2.
(a) Calculate the change in volume of 1.00 m^3 of water carried from the surface to this point in the ocean.


I set up an equation:
change in volume = [(change in pressure)(inital volume)] / Buoyance Force, which is [-(9.89 x 10^7 N/m^2)(1 m^3)] / (2.9 x 10^9 N), which finally equals -.034 m^3 for the change in volume, but that's wrong. Note: My TA gave me the value for the buoyance force.

Any suggestions would be greatly appreciated. Thank you! :smile:
 
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  • #2
Liquids are usually considered to be incompressible fluids, but in fact they are somewhat compressible. Under huge pressure the water mollecules will get closer together. You need to find some data on the compressibility of water. You might find this in terms of density of water as a function of pressure.

If you know the buoyancy at that depth, you could find the density from that.
 
Last edited:
  • #3
What would I need the density for?
 
  • #4
esinn08 said:
What would I need the density for?
Density is mass per unit volume. You are taking some mass of water that had a volume of 1m^3 at the water surface to a great depth. The mass is not going to change, but the volume is. If you know the new density you can calculate the new volume.
 
  • #5
I don't know how to find the density at this depth. This is an intro physics problem, so are there any "assumptions" I can make?
 
  • #6
esinn08 said:
I don't know how to find the density at this depth. This is an intro physics problem, so are there any "assumptions" I can make?
At an introductory level, you can assume it doesn't change at all. I tried to find some information about this on the internet, and the several links I followed all made reference to the UNESCO International Equation of State (1980) for sea water, but nobody shows you the equation. Here is a place that programmed a calculator based on the equation

http://fermi.jhuapl.edu/denscalc.html

and here is a place that gives a graph with an explanation that says the change in density is primarily due to changes in temperature and salinity

http://www.windows.ucar.edu/tour/link=/earth/Water/density.html&edu=high

Salinity does not apply in this case because of the wording of the problem. The only place I found that says there is a simple connection between density and pressure (and temperature) is here

http://www.lsbu.ac.uk/water/strange.html

Unless you have been given some information about the compressibility of water that is assumed to apply over a great range of pressures, assume it does not compress.
 
  • #7
Since this is an intro class, this HAS to be a simple [tex]P=\rho g h[/tex] problem. You know the pressure at and the depth (as well as g). Assume the density at the surface is [tex]\rho = 1000 \frac{kg}{m^3}[/tex]
 
  • #8
FredGarvin said:
Since this is an intro class, this HAS to be a simple [tex]P=\rho g h[/tex] problem. You know the pressure at and the depth (as well as g). Assume the density at the surface is [tex]\rho = 1000 \frac{kg}{m^3}[/tex]
[tex]P=\rho g h[/tex] assumes constant density at all depths. How is this going to give you a change in density?
 

Related to Pressure Problem (math error I think)

1. What is a pressure problem in math?

A pressure problem in math is a type of word problem that involves using the formula for pressure (P = F/A) to solve for one of the variables. It usually involves information about force, area, and pressure in real-world situations.

2. How do you solve a pressure problem?

To solve a pressure problem, you first need to identify the given information and what variable you are solving for. Then, use the formula P = F/A to set up an equation and plug in the values. Finally, solve for the unknown variable using algebraic operations.

3. What are the units for pressure?

The units for pressure depend on the system of measurement being used. In the SI system, pressure is measured in Pascals (Pa). In the Imperial system, it is measured in pounds per square inch (psi). Other units include atmospheres (atm) and millimeters of mercury (mmHg).

4. What are some common real-life examples of pressure problems?

Some common real-life examples of pressure problems include calculating the pressure exerted on a surface by an object, determining the force needed to compress a gas in a container, or finding the area needed for a given force to achieve a certain pressure.

5. How can I check if I solved a pressure problem correctly?

To check if you solved a pressure problem correctly, you can use dimensional analysis to make sure the units of your answer match the units of pressure (force/area). You can also plug your answer back into the original equation to see if it balances out.

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