# Modelling stream of water

peleus

## Homework Statement

Hi all,

I'll outline the situation first, then I'll ask about what I need.

Tank (designed by me / other students) which has no closed in top or bottom. Can be any shape, i.e. cylinder / cone / square etc etc. Made from cardboard with plastic bag in the middle acting as waterproof liner.

This sits atop of a reservoir which has a hole in the top of it (bottom of tank) to drain the water. Once in the reservoir it has two bungs in it (parallel to the floor), a 5mm and 10mm. Once these bung's are pulled obviously it drains the tank (downwards) and a stream of water shoots out (sideways), which we have to try and catch in a vessel below and a set distance away. The only variable we control is the size and shape of the tank. It contains 500ml of water.

You tell me :)

## The Attempt at a Solution

First things first, I'm not meant to understand how to do this yet. It's something that will be taught to us over the coming weeks, however I'm trying to do some research into the principles behind it now so I have a better understand anyway.

My understanding of how it works. Assuming a cylinder for a moment, the wider and shorter the tank is, the less pressure per cm^2 we have. As a result we will have a lower pressure stream shooting out of the bung. A taller skinnier cylinder will result in a higher pressure stream (higher force per cm^2). Because this is a cylinder we will have a drop off of pressure over time, from when it is full to where it is empty at a fairly linear rate.

A cone would perhaps be a better shape, we want to keep the water stream resulting on exactly one spot (or as close as possible) which means changing the surface area to less as we have less water to get the same force per cm^2.

Now - I have no idea how to go about modelling the problem. This is what I SUSPECT will be involved.

Working out the force per unit of area, so we can see how much pressure is one the hole in the bottom.

From this we should be able to work out some type of flow rate, so we now what speed the water will be shooting out at.

From there it should be fairly simple math modelling the water as gravity effects it, ignoring air resistance (which may be a big mistake in my design, should it matter indoors?)

I'm not particularly looking for someone to do up an entire spreadsheet modelling the problem for me (of course I wouldn't say no :P ) but really just wondering if someone can point me in the right direction to some good resources to learn those things I suspect are involved, or tell me if any of my assumptions about what is involved is wrong.

Thanks folks.