Calculate Time to Fill Bathtub with Volume Flow Rate

AI Thread Summary
To calculate the time to fill a bathtub, first determine the volume flow rate using the tap's velocity and the pipe's cross-sectional area. The flow rate in cubic meters per second can be calculated by multiplying the velocity by the area of the outlet. The time to fill the bathtub is then found by dividing the bathtub's volume by the flow rate. If considering temperature differences between hot and cold water, the calculation becomes more complex, involving differential equations. Understanding these principles allows for an accurate estimation of filling time.
Angello90
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Ok another stupid/smart question,

I got a bath with x m^3 volume. And a water flow rate of a tap is y m/s. I also know pressure and velocity. How can I calculate time to fill up bathtub? I know it's simple but I can not figure it out!
 
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You need to know the volume of water coming in per second, then it is easy. If you know the velocity you don't need to know the pressure. However that is not enough, you can have any volume of water at the same velocity/pressure.
 
Ok, so let's say the radius of pipe is r. This would give the area of outlet. Multiplying Q by A would give me (m/s) by (m^2), thus giving me volume of water coming out.

Does it make any sense?
 
Exactly, so you have m^3/s. If the bathtub fills up at x cubic meters then it takes x/Av seconds.

Now if it is hot or cold water then you have to account for the room temperature difference and it becomes a differential equation with an exponential coefficient in the solution.
 
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