Calculate Time to Fill Bathtub with Volume Flow Rate

[Angello90]

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!

 

[LostConjugate]

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.

 

[Angello90]

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?

 

[LostConjugate]

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.

 

[PJC01]

To calculate the time it takes to fill a bathtub, you will need to use the formula: Time = Volume / Flow Rate. In this case, the volume is given as x m^3 and the flow rate is given as y m/s. Therefore, the equation becomes: Time = x m^3 / y m/s.

To solve this equation, you will need to convert the units so that they are consistent. For example, if the volume is given in cubic meters (m^3), you will need to convert the flow rate to cubic meters per second (m^3/s). Once the units are consistent, you can simply divide the volume by the flow rate to get the time it takes to fill the bathtub.

Additionally, you may also need to consider the initial water level in the bathtub and the rate at which the water level rises. This can be calculated by dividing the flow rate by the area of the bathtub's opening. This will give you the depth of water that is added per second. Then, you can use this depth and the initial water level to calculate the time it takes to fill the bathtub completely.

I hope this helps and don't worry, there are no stupid questions when it comes to learning and understanding scientific concepts. Keep exploring and asking questions!