What Equation Calculates Pressure Needed to Empty a Tank in Under a Minute?

[Jason1083]

Homework Statement

Here is the scenario: If I have a cylindrical tank containg 30 liters of a substance. I want to determing the pressure/ energy necessary to empty the tank in 55-60 seconds through a 1/2" diameter outlet. In other words how much gas would I need to introduce to the tank to completely empty in the given time frame. What equation would I need?
Please tell me what other variables I would need and what equation?

Homework Equations

Trying to determine

The Attempt at a Solution

attempted to see if bernoulis equation could be utilized, but failed.

 

[anathema]

Hello there,

To determine the pressure/energy necessary to empty the tank in the given time frame, you will need to use the Bernoulli's equation along with the ideal gas law. The Bernoulli's equation states that the total energy of a fluid is constant along a streamline. In this case, the fluid is the substance in the tank and the streamline is the outlet.

The ideal gas law, on the other hand, relates the pressure, volume, and temperature of a gas. It can be written as P = nRT/V, where P is the pressure, n is the number of moles of gas, R is the ideal gas constant, T is the temperature, and V is the volume.

Using both equations, you can determine the pressure/energy necessary to empty the tank in the given time frame. However, you will also need to consider other variables such as the density of the substance, the viscosity of the substance, and the velocity of the substance as it flows through the outlet. These variables will affect the flow rate and ultimately the amount of gas needed to completely empty the tank.

I hope this helps. Let me know if you have any further questions. Good luck with your calculations!

 

[m2003]

There are a few different equations that could be used to solve this scenario, depending on the specific information and assumptions you are working with. However, one possible equation that could be used is the Torricelli's Law equation, which relates the volume, height, and flow rate of a liquid in a tank:

V = Ah, where V is the volume of liquid in the tank, A is the cross-sectional area of the tank, and h is the height of the liquid in the tank.

In this scenario, you could use this equation to solve for the initial height of the liquid in the tank (assuming it is initially full), and then use the given flow rate (determined by the outlet diameter and time frame) to calculate the necessary pressure/energy to empty the tank in the given time frame.

Other variables that may be needed include the density and viscosity of the substance in the tank, as well as any assumptions about the flow rate (e.g. assuming laminar flow). It may also be helpful to consider the effects of gravity and any potential losses due to friction or other factors.