# Calculus application (rate of water draining)

pezlet

## Homework Statement

This is actually just a problem that I'm trying to work out on my own (working on a little project).
The ultimate goal is that I'll know the amount of liquid coming out of the spigot per second, so I'll know roughly how long to open the spigot for to fill up a container of known volume.

I'm trying to find the rate of a liquid coming out of a spigot from a cylindrical container.
The known data will be:
height of container = 25cm
diameter of container = 12cm

density of liquid (if I need it)
height of liquid (if I need it)

## Homework Equations

volume of the container = 3600π cm^3 or 11310cm^3

## The Attempt at a Solution

I'm honestly pretty stumped from the start. I was thinking of a simple "draining tank problem" like we all go through in our first calculus course, however, I know neither dh/dt or dv/dt.

I can take some empirical data if I need to, but even then I'm not sure where to start.
I could open the spigot for 60 seconds and see how much liquid drained, but that rate will obviously change when there's less water.

I figured that since the spigot is at the bottom of the container, the force pushing down the water through the spigot is gravity acting on the mass of the overall liquid in the container at any given point. I can find the density of the liquid, because I think I will need that to solve the problem.

I honestly need more help setting up the problem than solving it. I've aced all of my calculus and my differential equations classes, but that was a couple years ago and the problem was always more obvious.

Any thoughts to point me in the right direction? Am I missing some desperately needed variables? If I need to take some measurements and retry the problem I absolutely can.

## Answers and Replies

Sourabh N
You can use the Bernoulli's equation. With some simplifying assumptions, the data you have will be enough to determine the rate of flow.

Start from the Bernoulli's equation and see how it looks for your system.

pezlet
That's a really good idea, I had heard of that and couldn't think of what it was called.

Thank you so much, that will definitely get me started.