Expression for the change in water height in a tank

In summary, the conversation revolves around a solved problem on change in water height with respect to time. The question arises about what would happen if the top of the tank is open to the atmosphere. The consensus is that nothing would change but the mass of air would be ignored in the calculation. The author also mentions the concept of one dimensional flow and its relevance to the exercise. Ultimately, the conversation concludes with a recommendation to study related background concepts.
  • #1
mech-eng
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frank w.png

Homework Statement



frank.png

Homework Equations




The Attempt at a Solution


There is solved problem on change in water height with respect to time. I understand it but there is the b part of the question. It asks that what's if the top of the tank is open to the atmosphere?

I think nothing would change but we would ignore the mass of the air in the calculation. So is it correct?

Thank you.

Source: Fluid Mechanics by Frank M. White
 
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  • #2
First reading caused a bit of confusion - I try to fix it below...
 
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  • #3
Hello,
In a second round I spent some more time reading all of your post -- and it turns out I can skip a great deal. It also turns out I have to read the lower part first and then the upper part :oops:. In the context of the exercise the fluid flow in terms of the velocity is given. Tank open or closed has an effect on the pressure behaviour but with these givens that does not affect the answer. Just before the exercise begins, the author uses the word 'realistic'. To me that doesn't apply to the exercise: I wouldn't know what a one dimensional inlet is. And usually fluid flow is pressure dependent.

My post #2 is now a bit out-of-context, so I'll erase it ... in order not to look too stupid for casual readers like me :smile:
 
  • #4
BvU said:
Hello,
In a second round I spent some more time reading all of your post -- and it turns out I can skip a great deal. It also turns out I have to read the lower part first and then the upper part :oops:. In the context of the exercise the fluid flow in terms of the velocity is given. Tank open or closed has an effect on the pressure behaviour but with these givens that does not affect the answer. Just before the exercise begins, the author uses the word 'realistic'. To me that doesn't apply to the exercise: I wouldn't know what a one dimensional inlet is. And usually fluid flow is pressure dependent.

My post #2 is now a bit out-of-context, so I'll erase it ... in order not to look too stupid for casual readers like me :smile:

Hello. I think author try to explain that the formula for conservation of flow rates is realistic. It doesn't directly said for the exercise but it is related to it as well.

It is very clear and easy to understand that the calculations never change when the top is open to the atmosphere. So why does author want to ask this?

I will continue to study background concepts related to this example such as one dimensional flow in this example.

Thank you.
 

FAQ: Expression for the change in water height in a tank

1. What is the equation for the change in water height in a tank?

The equation for the change in water height in a tank is Δh = Q/A, where Δh is the change in height, Q is the volume of water added or removed, and A is the cross-sectional area of the tank.

2. How do you calculate the cross-sectional area of a tank?

The cross-sectional area of a tank can be calculated by multiplying the length and width of the tank. If the tank has a different shape, such as a cylinder, the area formula for that shape should be used.

3. Does the change in water height depend on the size of the tank?

Yes, the change in water height is directly proportional to the size of the tank. A larger tank will require a greater volume of water to cause the same change in height compared to a smaller tank.

4. How does temperature affect the change in water height in a tank?

Temperature can affect the change in water height in a tank in two ways. First, as the temperature of the water increases, it expands and takes up more space, causing the water level to rise. Second, as the temperature of the tank itself changes, it can expand or contract, changing the overall volume of the tank and therefore affecting the water height.

5. Can other factors, such as air pressure, affect the change in water height in a tank?

Yes, other factors such as air pressure can affect the change in water height in a tank. Changes in air pressure can cause the water level to rise or fall due to the pressure exerted on the surface of the water. This is known as the barometric formula for water level change.

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