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If you have a situation in a steady state ("at rest") it would be pointless to introduce consideration of time dependence into any discussion or calculation relating to the problem. In fact, if you did include it, the first thing that would happen in your calculation would be that time variation would drop out of all consideration. So it would be pointless to include in the first place. On the other hand if you are calculating a changing situation, it would be foolish not to include time.

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Q: Why There is time dependent and independent equation.What is the need for this?
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Is Observing the change in salinity of water over time independent or dependent?

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