Can temperature affect the mass of water

[Amar_6193]

Hi there guys,

I'm conducting an experiment to calculate the mass flow rate of water. Bellow is a copy of the procedure:
1) Weigh the mass in kg of a container
2) Connect a flow meter to a tap (any source) with a pipe and insure the departure pipe goes into a sink
3) Open the tap an increase flow rate till first reading on flow meter is achieved (lets say 3 litres per minute)
4) Simultaneously divert the water exiting the flow meter into the container and start the stop watch
5) Continue till time x (40.54s random time)
6) Stop the stopwatch and divert the water back into the sink
7) Re-weigh the container to obtain the mass of the water

Now just to clarify, I wish to find out the mass flow rate in calculations so that I can verify that the flow meter is giving the correct reading and correctly calibrated.

Initially I presumed that it was quite simple to figure out, by just dividing the total mass of the water by the time taken to fill up the container I would obtain the mass flow rate. However others are telling me I have to involve temperature into the equation as this changes the density. I'm still confused to why this would matter, any help would be greatly appreciated.

 

[Hesch]

I have to involve temperature into the equation as this changes the density.

Yes, the density will be changed because the volume of the water will change due to temperature. As I remember the volume of the water will be smallest at 4C°, and thus the density will be highest at that temperature.

The mass of the water will not change due to temperature.

 

[Nugatory]

Flow meters usually measure the volume of liquid that flows per unit time. The mass that flows is that volume times the density; the density changes with the temperature, so the mass flow rate also does.

However, your first step should be to try calculating the approximate magnitude of the errors that will be introduced by these small changes in density. You may find that the effect of temperature fluctuations will be small enough to ignore for your purposes - I'd actually be somewhat surprised to find that they aren't swamped by other sources of uncertainty in your setup.

 

[Orodruin]

Since you are not using the volume flow rate (and indeed you should not), the density never enters into the problem. You can compute the density by relating it to the volume flow rate ...

 

[jim hardy]

You didn't say what type flowmeter you're using.

Bernoullis equation includes a term for density. So, if you're using a differential pressure type meter like a venturi there'll be a density term under the radical.
H = v²/2g
√H*2g = v
2g being constant at any given location,
√H is proportional to velocity.
since less dense fluid has to move faster to get the same mass through the same area
v will be linear with 1/density
so your ΔH term (difference in pressures between the venturi inlet and throat diameters) will vary with density.
.
So,
you should know at what density you made your measurements so that you can correct for winter vs summer experiments.
If you're using a positive displacement meter like a nutating disk the density correction will be linear of course.

ASME publishes a most excellent reference book with the simple title "Fluid Meters".
https://www.asme.org/products/books/fluid-meters-theory-application-sixth

 

[Amar_6193]

Thank you all very much for your input, here are a few key points I would like to say from your comments,

Firstly the experiment is set up so that I can use any flow meter and it's the verification of the reading that is more important.
Secondly, and most importantly is there an equation I can use to find the exact density of water at a know temperature. Everyone says that at 4 degrees the density of water is 1000kg/m^3 however I need this value to be more accurate. I have spent a large amount of time trying to tackle this problem yet everywhere I look there just seams to be tables with set values of temperature used (e.g. 4, 5, 6, 7, 8, degrees) however if I know that the temperature is 4.563 degrees I wish to be able to find the exact density.

Finally I would like to thank you all for your current input and would be truly grateful if you could help me out with my current queries.

 

[jim hardy]

everywhere I look there just seams to be tables with set values of temperature used (e.g. 4, 5, 6, 7, 8, degrees) however if I know that the temperature is 4.563 degrees I wish to be able to find the exact density.

Is interpolation not close enough? To how many significant figures are you working? Beyond three you need to start accounting for effects like local gravity ..

Exact calculations get too complicated for me, i always just used the ASME steam tables.

Here's a link to the International Association for the Properties of Water and Steam's exhaustive treatment.
http://www.iapws.org/relguide/IF97-Rev.pdf
http://www.iapws.org/relguide/Supp-VPT3-2014.pdf