Time required to empty a liquid filled contaier through an orifice

In summary, the conversation discusses the process of emptying a spherical shell filled with liquid through a small hole. Bernoulli's equation and Torricelli's Law are suggested as potential methods to find the exit speed, and it is mentioned that a hole should also be present at the top of the shell. It is also noted that this process is similar to a Zahn cup, and that it is not a homework question but rather a personal inquiry.
  • #1
supratim1
Gold Member
279
1
This is not a homework question. I am trying to figure it out myself.

Let a spherical shell of radius R be filled with a liquid (full). Now let a small hole of area A be made at the bottom of the shell. Find the time required to empty the shell completely.
 
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  • #2
hi supratim1! :wink:

use Bernoulli's equation along a streamline to find the exit speed …

what do you get :smile:

(oh, and i think you'll need a hole at the top of the shell, also! :biggrin:)
 
  • #3
can't we use the Toricelli's Law? I too think a hole should be there at top.
 
  • #4
What you're describing is very similar to a Zahn cup.
 
  • #5
supratim1 said:
This is not a homework question.


It indeed is... i am your classmate and i know it!

And yes, consider the top is open (you can imagine it to have a hole)
 

1. How does the size of the orifice affect the time it takes for a liquid-filled container to empty?

The size of the orifice plays a significant role in the time it takes for a liquid-filled container to empty. The larger the orifice, the faster the liquid will flow out of the container. This is because a larger orifice allows for a greater volume of liquid to pass through at once.

2. Does the viscosity of the liquid affect the time required to empty a container?

Yes, the viscosity of the liquid does affect the time required to empty a container. Viscosity refers to the resistance of a liquid to flow. Liquids with higher viscosity, such as honey or molasses, will take longer to flow out of a container compared to liquids with lower viscosity, such as water or oil.

3. What other factors besides orifice size and liquid viscosity can affect the emptying time of a container?

Other factors that can affect the emptying time of a container include the shape and size of the container, the height of the liquid in the container, and the presence of any obstructions or bends in the orifice. These factors can impact the flow rate of the liquid and ultimately affect the time it takes for the container to empty.

4. Is there a mathematical formula to calculate the time required to empty a liquid-filled container through an orifice?

Yes, there is a mathematical formula known as Torricelli's law that can be used to calculate the time it takes for a container to empty through an orifice. This formula takes into account the orifice size, liquid density, and height of the liquid in the container to determine the flow rate and ultimately the emptying time.

5. Can the time required to empty a container be altered by changing the height of the liquid in the container?

Yes, changing the height of the liquid in the container can alter the time it takes for the container to empty. According to Torricelli's law, the higher the liquid level, the greater the pressure at the orifice, resulting in a faster flow rate. This means that a container with a higher liquid level will empty faster than a container with a lower liquid level, all other factors remaining the same.

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