# Homework Help: Momentum of a vertical stream of water hitting a surface

1. May 4, 2010

### velvet

Hello there, I have a question, I wonder if you can help me.

1. The problem statement, all variables and given/known data

I am using scales to measure the volume of liquid coming from a bottle, and then differentiating this volume to give flow rate. The bottle emits a constant flow rate and I hold it so that the stream falls vertically, collecting in a jug on the scales. When the stream of liquid initially hits the scales, it creates a momentum artefact, i.e. a 'spike' in the flow rate which then settles down to the correct flow rate. Obviously this spike also appears at the end of the flow, but this time negative.

I am investigating the size of this artefact when the bottle is held at different heights from the scales, and if it can be modelled. I would like to come up with an equation to describe the relationship but I am not sure how to go about this.

2. Relevant equations

Acceleration due to gravity, g = 9.81 metres per second squared
Force = rate of change of momentum
Momentum = mass x velocity
Flow rate from bottle = constant
1litre = 1kg

3. The attempt at a solution

I have poured the water from several different heights, and calculated the area under the flow rate 'spike', i.e. the volume artefact. The area under the artefact seems to increase with the square root of the height. (It looks like that sort of relationship but I am not sure. I believe if I plotted 'height of bottle' against 'area under artefact', the curve would tend towards becoming flat, which a height curve does not.)

I think my problem is that the volume of water in the jug is constantly changing so I am not sure which mass to use in the calculations.

Many thanks :)

2. May 4, 2010

### Mindscrape

How dramatic is the spike? Maybe you could get a graph and post a jpg file of what you're seeing. My hypothesis is that when you first hit the scale you are seeing some recoil from the first drops that hit the scale, which gives you more then a factor of 1, but less than a factor of two, for the change in momentum that translates to force. Once you have more liquid on the scale, the substance is no longer recoiling because of the liquids cohesion.

3. May 5, 2010

### velvet

Hello, thank you for your reply.

This graph shows the flow rate curves, the curve on the left is with the bottle held closest to the scales and that on the right, the farthest away (those that don't increase are anomolies because I have done it again more carefully since and with repeats):

http://i119.photobucket.com/albums/o158/alisonbray/Flowratevtime.png

This graph shows the relation between area under spike (volume artefact) and distance between bottle nozzle and impact surface:

http://i119.photobucket.com/albums/o158/alisonbray/Heightvartefact.png

Many thanks :)

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• ###### Height v artefact.png
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