# How pressure and temperature affects volumetric flow?

• Micko
In summary, the conversation discusses the behavior of fluids under pressure and temperature changes. It is mentioned that liquids are considered incompressible, so density and volumetric flow rate do not change. However, temperature does affect both liquids and gases, causing them to expand and the volumetric flow rate to increase. The conversation then delves into a specific example of a pipeline used to transport hot water, questioning the order of magnitude of the volumetric flow rate and the potential decrease in flow on the return end due to temperature changes. The conversation also addresses the issue of thermal effects on volumetric flow rate meters and suggests using tables of specific volumes at reference temperatures and pressures. Finally, a table of water properties is provided, showing a slight expansion of water
Micko
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.

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

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## 1. How does pressure affect volumetric flow?

Pressure and volumetric flow are directly related. As pressure increases, the volume of a gas or liquid decreases, resulting in a higher volumetric flow rate. This is known as Boyle's Law.

## 2. How does temperature affect volumetric flow?

Temperature and volumetric flow are also directly related. As temperature increases, the molecules of a gas or liquid move faster and take up more space, resulting in a higher volumetric flow rate. This is known as Charles's Law.

## 3. What is the relationship between pressure and temperature in terms of volumetric flow?

Pressure and temperature have an inverse relationship when it comes to volumetric flow. As pressure increases, temperature decreases, and vice versa.

## 4. How do changes in pressure and temperature affect the viscosity of a fluid?

Changes in pressure and temperature can affect the viscosity of a fluid. As pressure increases, the viscosity of a fluid may increase as well. As temperature increases, the viscosity of a fluid may decrease.

## 5. How can pressure and temperature be manipulated to control volumetric flow?

Pressure and temperature can be manipulated to control volumetric flow by adjusting one or both factors. For example, to increase volumetric flow, pressure can be increased or temperature can be decreased (or a combination of both). This is used in various industrial processes to regulate the flow rate of gases and liquids.

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