Change of of the pressure of water inside a container

  • #1
I am having difficulty solving an exercise prepared by our professor for hydrodynamics. I am unsure if Laplace pressure is the correct way to calculate the pressure inside. It comes to my mind that I should've used the equation for hydrostatic pressure instead (##P=P_0+\rho gh##). However, the height of the container above the ground is not given. So I considered that the unknown is the pressure exerted by the water on the container walls.

Homework Statement


5 liters of water is enclosed inside a spherical container made of 1cm thick aluminum. The whole system is in thermal equilibrium at room temperature (I took it 25 degrees) and atmospheric pressure. The temperature of the water is raised by 5K. I need to find the change of pressure of the water inside the container after the change of temparature.

Homework Equations


Laplace pressure:
$$\Delta P=P_{inside}-P_{outside}=\gamma\frac{2}{r}$$
where ##\gamma## is the surface tension of the liquid and r is the radius.

The Attempt at a Solution


I first attempted to calculate the pressure inside the container using the equation for Laplace Pressure. I took ##\gamma## (surface tension of the Water) as 72 which is correct for 25 degrees Celsius. Since the aluminum container is 1cm thick, I contributed that to the radius thus; ##P_{inside}=P_{outside}+\gamma\frac{2}{(r+1cm)}##. For the increased pressure, I calculated the same, but this time with ##\gamma## for water at 30degrees Celsius (5K temp. added). Then I simply calculated the difference between these two pressures.


My questions are:
1)Is my method correct for this case of aluminum container or it only works on expanding bubbles?
2)What should I have done regarding the thickness of the aluminum?
3) Is there another way to calculate the pressure difference?
 

Answers and Replies

  • #2
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Expansivities of H2O and Al are equal?
 
  • #3
Expansivities of H2O and Al are equal?
The coefficients of volume expansion are not given. Are you hinting I should be working on towards that area?
 
  • #4
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coefficients of volume expansion are not given
It's a thought;
our professor for hydrodynamics
implies some degree of academic freedom/latitude.
 
  • #5
I meant exercise for hydrodynamics prepared by our professor. Excuse me for that please.
 
  • #6
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  • #7
If that's not how I should be saying it, I meant that as "the lecturer that was assigned for our Physics II class". The figures of speech can vary in different languages. I'm studying in Europe, please pardon me for my mistake.
 
  • #8
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You should not be considering surface tension, since there is no free surface. This is a thermal stress problem, involving the aluminum. I guess you are supposed to (a) neglect gravity and (b) assume that the water temperature increases, but not the aluminum temperature. The first step is to determine the inside radius of the sphere. What is the value of that radius. If the water were not constrained by the aluminum sphere but, instead, were able to expand freely, how much would the radius increase under the temperature increase of 5C?
 
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