- #1
Baris Kalfa
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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.
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.
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.
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?
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?
