How pressure and temperature affects volumetric flow?

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Discussion Overview

The discussion revolves around how pressure and temperature changes affect the volumetric flow rate of fluids, particularly in the context of fluid mechanics. Participants explore theoretical and practical implications of these changes, including the behavior of liquids and gases under varying conditions, and the specific case of hot water transport in a pipeline system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that liquids are often treated as incompressible, suggesting that density and volumetric flow rate remain constant under pressure changes.
  • Another participant argues that temperature increases lead to expansion in both liquids and gases, which could increase volumetric flow rates, while decreases in temperature would have the opposite effect.
  • A specific scenario is presented involving a pipeline transporting hot water, with parameters given for pressure and temperature at both the sending and return ends, raising questions about the expected change in flow rate.
  • Some participants express skepticism about the magnitude of flow rate differences, suggesting that a 15 m³/h variation seems excessive unless boiling occurs.
  • One participant challenges the idea that volumetric flow rates in must equal volumetric flow rates out, emphasizing the importance of mass flow rates in steady state conditions.
  • Another participant acknowledges a previous misunderstanding regarding flow rates and expresses a realization about the conservation of mass in fluid dynamics.
  • Data on the density of water at various temperatures is shared, indicating that volumetric changes due to temperature variations are relatively small but significant enough to warrant consideration in practical applications.
  • Links to external resources for further information on water properties and thermal expansion are provided by participants.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between volumetric flow rates in and out of a system, with some asserting that they must be equal while others argue that mass flow rates are the critical factor. There is no consensus on the expected magnitude of flow rate changes due to temperature differences, with some participants questioning the validity of a 15 m³/h difference.

Contextual Notes

Participants reference specific temperature and pressure conditions, as well as the thermal expansion coefficients of water, but the discussion remains open-ended regarding the exact implications of these factors on flow rates. There are also mentions of potential measurement inaccuracies related to thermal effects on flow rate meters.

Micko
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Hello guys,
I'm reading about fluid mechanics and learning how fluid behaves when there is a pressure and temperature change. I found this: „Liquids are deemed incompressible and therefore, density and the volumetric flow rate do not change“,
and this: „Temperature affects liquids and gases in the same way. Both liquids and gases
expand with rising temperature and the volumetric flow rate will therefore
increase. A decrease in temperature will have an opposite effect.“ I wonder what is order of mangitude of volumetric flow?
For example, if I have pipeline which is used to transport hot water for purpose of warming some object and pressure and temperature on transmitting end are: p = 15 bar, T = 90 deg Celz, and on it's return (for purpose of heating again) parameters are p = 1 bar and T = 50 deg Celz, what is order of change if on sending end flow was 200 m^3/h (kubic meters per hour)? Is this temperature change likely to cause decrease in flow on it's return end (return pipe) more than, say, 1 m^3/h if all other leaks and losses are negligible?
I need to know this in order to estimate losses in pipeline because I have two measurement places (one place where hot water is sent through pipeline, and on it's return end) and differece is about 15 m^3/h. Temperature differece is about 40 deegrees Cel., I doubt that difference in flow is greater of 1 m^3/h due to temperature change.
 
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Micko said:
Hello guys,
I'm reading about fluid mechanics and learning how fluid behaves when there is a pressure and temperature change. I found this: „Liquids are deemed incompressible and therefore, density and the volumetric flow rate do not change“,
and this: „Temperature affects liquids and gases in the same way. Both liquids and gases
expand with rising temperature and the volumetric flow rate will therefore
increase. A decrease in temperature will have an opposite effect.“ I wonder what is order of mangitude of volumetric flow?
For example, if I have pipeline which is used to transport hot water for purpose of warming some object and pressure and temperature on transmitting end are: p = 15 bar, T = 90 deg Celz, and on it's return (for purpose of heating again) parameters are p = 1 bar and T = 50 deg Celz, what is order of change if on sending end flow was 200 m^3/h (kubic meters per hour)? Is this temperature change likely to cause decrease in flow on it's return end (return pipe) more than, say, 1 m^3/h if all other leaks and losses are negligible?
I need to know this in order to estimate losses in pipeline because I have two measurement places (one place where hot water is sent through pipeline, and on it's return end) and differece is about 15 m^3/h. Temperature differece is about 40 deegrees Cel., I doubt that difference in flow is greater of 1 m^3/h due to temperature change.
Here is some data on the thermal expansion coefficients of water at various temperatures.

http://hypertextbook.com/physics/thermal/expansion/

Water is most dense at 4 degrees, so the coefficient is zero and changes sign at that temperature. The numbers give the fractional change in volume per degree change in temperature. As you can see, the effect is not very big.

As for volumetric flow rates, I don't think the density change makes any difference in any steady state situation. If you have hot water flowing down a pipe to a cooler end with a steady state temperature and pressure profile there will be a density variation, but the density at any point will be constant. Whatever volume of water you add to one end will come out the other end. If less is coming out than you are putting in, you have a leak.

What might be more of a problem is thermal effects on the volumetric flow rate meter. I don't know how the meter works, but I would think its own thermal expansion could be a problem. I wonder if it is truly measuring volume, or making some other measurement and converting that to a volume equivalent.
 
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OlderDan, I'm inclined to disagree with your analysis of the situation. The volumetric flow rate in is not necessarily equal to the volumetric flow rate out for steady state conditions. Instead the mass flow rate in must be equal to the flow rate out for steady state. As a student of thermodynamics, I know this will make a difference. If all else fails, just use a table of specific volumes at your reference temps and pressures.
 
He is wrong in that, but at the same time I think that a variation of 15 m^3/h is too much for water as he said, unless it is boiling over there.
 
sicjeff said:
OlderDan, I'm inclined to disagree with your analysis of the situation. The volumetric flow rate in is not necessarily equal to the volumetric flow rate out for steady state conditions. Instead the mass flow rate in must be equal to the flow rate out for steady state. As a student of thermodynamics, I know this will make a difference. If all else fails, just use a table of specific volumes at your reference temps and pressures.
You are quite right. I don't even know what made to think about this problem again, but it suddently struck me a few hours ago how silly it was for me to think the volumetric flow rate would not change. That would clearly be a violation of conservation of matter. I'm sorry it took so long for the light to dawn on me, but I'm glad to see somebody else caught my error.
 
Micko,

Here is the saturated liquid water density and the compressibility as a function of temperature,
as I found it in my files:


T[°C] ... rho[kg/m²] ... d(rho)dT
0 ... 999.793 ... 0.0590
1 ... 999.852 ... 0.0414
2 ... 999.893 ... 0.0243
3 ... 999.917 ... 0.0078
4 ... 999.925 ... -0.0081
5 ... 999.917 ... -0.0236
6 ... 999.893 ... -0.0386
7 ... 999.855 ... -0.0532
8 ... 999.802 ... -0.0673
9 ... 999.734 ... -0.0811
10 ... 999.653 ... -0.0944
20 ... 998.16 ... -0.2112
30 ... 995.608 ... -0.3057
40 ... 992.183 ... -0.3854
50 ... 988.008 ... -0.4549
60 ... 983.175 ... -0.5169
70 ... 977.748 ... -0.5732
80 ... 971.778 ... -0.6253
90 ... 965.304 ... -0.6740
100 ..... 958.354 ... -0.7203


You may find this in a table of water properties or maybe on the http://www.iapws.org/" .
The http://webbook.nist.gov/chemistry/" is also a wonderful place to go.

You will notice the slight expansion from 4°C to 0°C. It is small but enough to break a bottle!
From 4°C to 100°C you will notice an expansion by about 5% . This will increase the volumetric flow for higher temperatures. Therefore you need an expansion bottle in your central heating facility.
The attached file is a plot of the compressibility vs temperature.

Michel
 
Last edited by a moderator:

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