How pressure and temperature affects volumetric flow?

  1. 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.
     
  2. jcsd
  3. OlderDan

    OlderDan 3,031
    Science Advisor
    Homework Helper

    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.
     
  4. 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.
     
  5. Clausius2

    Clausius2 1,479
    Science Advisor
    Gold Member

    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.
     
  6. OlderDan

    OlderDan 3,031
    Science Advisor
    Homework Helper

    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.
     
  7. 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 IAPWS web site.
    The NIST Chemistry WebBook 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: Nov 22, 2011
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?