Need help with a unsteady state mass balance problem

In summary, the problem is finding out the amount of time it takes to drain a 12oz soda can through the shotgun method. The method involves opening the tab on top of the can and then punching a hole at the bottom to drain the soda out. The velocity out obviously changes as the height of the fluid inside the can changes. I've taken the point on the top surface of the fluid (having p=1atm) and the point on the bottom, at the draining hole. Im looking for dM/dt or dV/dt. Can I assume the velocity on the surface=0 in comparison to the velocit of water at the bottom hole? I've come up with dV/dt=A2*Vel
  • #1
jeff25111
3
0
if anybody can help,
the problem is finding out the amount of time it takes to drain a 12oz soda can through the shotgun method. this method of draining involves opening the tab on top of the can and then punching a hole at the bottom to drain the soda out.the velocity out obviously changes as the height of the fluid inside the can changes. I've taken the point on the top surface of the fluid (having p=1atm) and the point on the bottom, at the draining hole.
im looking for dM/dt or dV/dt. can i assume the velocity on the surface=0 in comparison to the velocit of water at the bottom hole?
ive come up with dV/dt=A2*Vel. exit
ive used the mechanical energy balance to solve for ave vel exit=sqrt(4*grav*y)*Area(of exit hole)
pls tell me if I am approaching this problem correctly.would appreciate any input
 
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  • #2
Sounds like you're on track. I think the Bernoulli Equation would yield you a good approximation.

Find the velocity of the fluid exiting out of the hole and multiply that by the cross-sectional area of the hole to find the flow rate. Then it's just a matter of how much fluid is in the can divided by the flow rate.
 
  • #3
jeff25111 said:
ive come up with dV/dt=A2*Vel. exit
ive used the mechanical energy balance to solve for ave vel exit=sqrt(4*grav*y)*Area(of exit hole)

The exit velocity using Bernoulli would be v = sqrt(2*g*h),

where,

h = height of the fluid column
g = gravitational accel.

The flow rate would then be the area times the velocity.
 
  • #4
You know, on second thought I'm not sure if you could use that equation since you have such a small hole in the top of the can.
 
  • #5
i wouldn't know which points to choose if the pressure on top is unknown. i don't think i can assume that the pressure on the draining hole is equal to the atmospheric pressure either..just at a loss
 
  • #6
The pressure on top is atmospheric pressure unless you are applying more. If you are just punching a hole in the top of the can, then it's 1 ATM like you already stated.

The pressure at the outlet, where the fluid is draining to, is 1 ATM also since it is flowing freely.
 

1. What is a unsteady state mass balance problem?

A unsteady state mass balance problem is a type of problem commonly encountered in chemistry and other sciences that involves calculating the change in the concentration or amount of a substance over time as it undergoes a chemical reaction or physical transformation. This type of problem requires understanding of concepts such as reaction rates, stoichiometry, and conservation of mass.

2. How do I approach solving a unsteady state mass balance problem?

The first step in solving a unsteady state mass balance problem is to clearly define and understand the problem. This includes identifying the substances involved, the reactions or processes occurring, and any known or unknown quantities. From there, the problem can be approached using mathematical equations and principles such as the law of conservation of mass and the rate law for the reaction.

3. What are the key concepts to understand when working on a unsteady state mass balance problem?

Some key concepts to understand when solving a unsteady state mass balance problem include reaction rates, stoichiometry, and the law of conservation of mass. Reaction rates refer to the speed at which a reaction occurs, and can be affected by factors such as temperature, concentration, and the presence of catalysts. Stoichiometry involves the relationship between reactants and products in a chemical reaction, and is important for determining the amount of each substance involved. The law of conservation of mass states that matter cannot be created or destroyed, so the total amount of each element must remain constant throughout the reaction.

4. How can I check if my solution to a unsteady state mass balance problem is correct?

One way to check the accuracy of your solution to a unsteady state mass balance problem is to perform a mass balance check. This involves calculating the total mass of each element before and after the reaction, and ensuring that they are equal. Additionally, it can be helpful to double check the units and significant figures in your calculations to ensure they are correct.

5. Are there any common mistakes to avoid when solving a unsteady state mass balance problem?

One common mistake to avoid when solving a unsteady state mass balance problem is not properly setting up the problem or identifying all of the relevant information. It is important to clearly define the problem and all of the substances involved, as well as any known or unknown quantities. Another mistake to avoid is not paying attention to units and significant figures throughout the problem, as this can lead to incorrect solutions. It is also important to double check your calculations and solution for accuracy.

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