# Can temperature affect the mass of water

• Amar_6193
In summary: With 3 significant figures.In summary, the experimenter is trying to figure out the mass flow rate of water. They weigh a container filled with water, and then connect a flow meter to a tap and increase the flow rate until the first reading is achieved. They divert the water into the container and start the stopwatch. They continue until the time is x (40.54 seconds). They stop the stopwatch and re-weigh the container to find the mass of the water. They say that the density changes with temperature, so they need to include temperature into the equation. They say that if they know the temperature, they can find the density. They suggest looking for a book with the title "
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.

Amar_6193 said:
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.

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.

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 ...

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

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.

Amar_6193 said:
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

Last edited by a moderator:

## 1. Does the temperature of water affect its mass?

Yes, the temperature of water can affect its mass. When water is heated, its molecules gain energy and move faster, causing them to take up more space and increase the volume of the water. This results in a decrease in mass per unit of volume, which means that warm water has a lower density and therefore a lower mass compared to cold water.

## 2. How does temperature affect the density of water?

As mentioned before, when water is heated, its molecules move faster and take up more space, resulting in a decrease in density. As a general rule, the warmer the water, the lower its density. This means that warm water will float on top of cold water because it is less dense.

## 3. Can water have a negative mass due to temperature?

No, water cannot have a negative mass due to temperature. While heating water can decrease its density and therefore its mass per unit of volume, the overall mass of the water will still remain positive. In extreme cases, such as when water is heated to its boiling point, the water will turn into gas and its mass will decrease due to the loss of molecules.

## 4. How does temperature affect the weight of water?

Temperature does not directly affect the weight of water. Weight is a measure of the force of gravity on an object, and it remains constant regardless of the temperature of the water. However, since the mass of water can be affected by temperature, the weight of a specific volume of water may change.

## 5. Is the change in mass of water due to temperature significant?

The change in mass of water due to temperature can vary depending on the starting temperature and the amount of heat added. In most cases, the change in mass is relatively small and may not be significant for everyday purposes. However, for scientific experiments or precise measurements, it is important to take into consideration the effects of temperature on the mass of water.

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