Fluid Dynamics: Answering Pressure in a Full Tank

In summary, the conversation discusses the concept of a full tank of water with a valve at the bottom being opened and the pressure that the tank will reach as the water drains. It is mentioned that the water will vaporize due to the lack of pressure, but there is uncertainty about the calculation needed. The answer is later revealed to be based on atmospheric pressure and the density and height of the water. It is also noted that at a certain height, the minimum pressure will be below the vapor pressure of water, making the vessel not possible.
  • #1
shannajo03
2
0
I understand the concept of this question, I think, but I don't know how to go about getting an answer.

A tank is completely full of water with no air. A valve at the bottom is opened, while one on top remains closed. What is the lowest pressure that the tank will reach. From valve to valve the height is 30ft.

I understand that as the water drains, it will pull a vacuum inside the tank, which will eventually collapse at a low enough pressure. I also know that the water will vaporize at some point due to the lack of pressure in the tank, but I don't know if they want the vapor pressure (no temp was given) or if there is some calculation to do.

Any guidance is appreciated!
 
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  • #2
For anyone who is wondering, I found out the answer. You assume atmospheric pressure pushes up into valve B, so the pressure in the tank is 14.7psi-(rho)gh where rho is the density of water, g is gravitational accel. (32.2ft/s^2), and h is 30ft. The point was that on the second part (h=40ft), the minimum pressure is below the vapor pressure of water, so the vessel is not possible at that height.
 
  • #3


I would approach this problem by first understanding the principles of fluid dynamics and pressure. Pressure is defined as the force per unit area and is affected by the height of the fluid column and the density of the fluid.

In this scenario, the tank is completely full of water with no air, so the pressure at the bottom of the tank will be equal to the weight of the water column above it. This pressure is known as hydrostatic pressure and can be calculated using the equation P = ρgh, where ρ is the density of the fluid (in this case, water), g is the acceleration due to gravity, and h is the height of the fluid column.

In this case, the height of the fluid column is given as 30ft. Assuming standard conditions (density of water = 1000 kg/m3, acceleration due to gravity = 9.8 m/s2), the pressure at the bottom of the tank would be approximately 294 kPa.

As the water drains from the tank, the pressure at the bottom will decrease due to the decreasing height of the fluid column. However, it is important to note that the pressure will not reach zero until the tank is completely empty.

Regarding the vaporization of water, the vapor pressure of water depends on the temperature, so without that information, it is difficult to determine the lowest pressure that the tank will reach. However, it is safe to assume that the vapor pressure of water at room temperature (25°C) is approximately 3.17 kPa.

In summary, the lowest pressure that the tank will reach will depend on the temperature and the vapor pressure of water. However, based on the given information, the pressure at the bottom of the tank will decrease as the water drains, but it will not reach zero until the tank is completely empty.
 

1. What is fluid dynamics?

Fluid dynamics is the study of the movement of fluids, including liquids and gases, and how they interact with their surroundings. It involves analyzing the forces and pressures on fluids in order to understand their behavior.

2. How does pressure affect fluids in a full tank?

Pressure plays a crucial role in determining the behavior of fluids in a full tank. As the tank is filled, the pressure of the fluid at the bottom increases due to the weight of the fluid above it. This pressure is distributed evenly throughout the fluid, causing it to exert a force on all sides of the tank.

3. How can pressure be measured in a full tank?

Pressure can be measured in a full tank using a pressure gauge or sensor. These devices measure the force exerted by the fluid on the walls of the tank and provide a reading in units of pressure, such as pounds per square inch (psi) or pascals (Pa).

4. What factors affect the pressure in a full tank?

The pressure in a full tank is affected by several factors, including the volume and density of the fluid, the height of the fluid column, and the shape and size of the tank. The type of fluid and its temperature can also impact the pressure.

5. How does the pressure in a full tank change as the fluid is drained?

The pressure in a full tank decreases as the fluid is drained due to the decrease in fluid volume and height. This results in a decrease in the weight of the fluid and therefore a decrease in the force exerted on the walls of the tank. The rate at which the pressure decreases will depend on the fluid's density and the size and shape of the tank.

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