# Temperature of fluid flowing through pipe

• Jay_
In summary, the temperature change when a fluid flows through a pipe from one end to another is dependent on the following parameters: -cross-sectional diameter of the pipe-viscosity-volumetric flow rate-specific heat of the fluid-length of the pipe
The values seem correct to me. I did the calculations by hand before and verified them in the code (like the mixing rules for instance). But since I haven't done this before, I wanted you to check if the values are inside the typical values.

Jay_ said:
The values seem correct to me. I did the calculations by hand before and verified them in the code (like the mixing rules for instance). But since I haven't done this before, I wanted you to check if the values are inside the typical values.
Well done!

What about the calculated physical properties (conductivity, viscosity, heat capacity) as a function of temperature from your relationships? Do they match up as closely as you would like with the values in tables, or from graphs. For example, there are graphs of heat capacity as a function of temperature in some books. Is that a close enough match for you? Density, of course, comes from the ideal gas law, so that's no problem, right?

Chet

I just did a random check. I checked it for viscosity of CO2 at two different temperatures. And heat capacities for Air and apart from that I kept faith in the equations because they seem to be from credible sources. The equations from Perry I double checked for each of them at random temperatures.

Then it looks like you're ok.

Chet

Hey Chet,

Congratulations on becoming Mentor, you have certainly been mine through this, and I will mention you the report.

I am back here because I am still feeling dicey about the equation for the Nusselt number inside the pipe.

In the pdf attached, they seem to use the Seider-Tate relation (Page 3, eq. (1)). I would have overlooked it, but its the proportionality constant values. We are using 0.003 to 0.004, and they Seider-Tate uses a value as high as 0.027, almost 6 to 9 times as high!

Since, we have put all this effort, I don't want us to mess up on this one aspect. You mentioned that these equations are based off on collected data, but I can't imagine why the proportionality constants would vary so much.

Jay_ said:
Hey Chet,

Congratulations on becoming Mentor, you have certainly been mine through this, and I will mention you the report.

Thanks very much.
I am back here because I am still feeling dicey about the equation for the Nusselt number inside the pipe.

In the pdf attached, they seem to use the Seider-Tate relation (Page 3, eq. (1)). I would have overlooked it, but its the proportionality constant values. We are using 0.003 to 0.004, and they Seider-Tate uses a value as high as 0.027, almost 6 to 9 times as high!

Since, we have put all this effort, I don't want us to mess up on this one aspect. You mentioned that these equations are based off on collected data, but I can't imagine why the proportionality constants would vary so much.

Seider-Tate will always give a lower value of Nu than 0.004 (within its Re range of applicability). Also, check out the exponent on the Re in Seider-Tate. If you're not sure about all this, just calculate the Nu both ways for different Re's and compare them.

Chet

What use it it comparing them? Let's take the value we got 6717 for Re, and 0.68 for Pr.

BSL gives me : Nu = 23.627,
Seider-Tate gives me : Nu = 27.37

Okay, I assumed the values are going to be much different. In any case, which one do I consider and why?

What's the required Re range for Seider-Tate?

Chet

Wikipedia says it must be above 10,000. Let's consider that Re = 10000.

Taking the log of the Nusselt number equations in both cases :

BSL : log(Nu) - (1/3)*log(Pr) = log(0.004) + log(10,000) = 1.60206

Seider-Tate : log(Nu) - (1/3)*log(Pr) = log(0.027) + 0.8*log(10,000) = 1.63136

Is that difference acceptable? The disturbing thing about that graph in BSL is :

1. The line of the graph is thick, leading to inaccuracies
2. At Re = 60,000 the line is actually below 0.003, which is another inaccuracy. At Re = 10,000 also, its below 0.004 - that means the Nusselt numbers are smaller than calculated - that would have been comforting. But the problem being that the Nu by Seider-Tate comes to be bigger. If it came to be smaller, I could have thought of it as the inaccuracy in the line of the graph (and my vision).

-------------------------------------------------------------------------------------

Also!

Since I have temperature based polynomials for the viscosity of the gas, I could as well include the viscosity factor in the calculations right?

viscosity factor = (mu_bulk/mu_boundary_layer)

Correct?

Here, the temperature of the bulk gas is the T_gas_estimated, and the denominator is the INNER film temperature right? I am just going to include the (viscosity factor)^0.14 in the Nusselt number equation.

And which would be a better pick, Seider-Tate or BSL? If Sieder-Tate is more accurate, I want to use BSL for Nusselt numbers up to the value of 10,000 and then use Sedier-Tate from there on. But which is more accurate in your opinion?

Last edited:
Jay_ said:
Wikipedia says it must be above 10,000. Let's consider that Re = 10000.

Taking the log of the Nusselt number equations in both cases :

BSL : log(Nu) - (1/3)*log(Pr) = log(0.004) + log(10,000) = 1.60206

Seider-Tate : log(Nu) - (1/3)*log(Pr) = log(0.027) + 0.8*log(10,000) = 1.63136

Is that difference acceptable?
The difference in Nu is only 7%. This compares with the 20-30% uncertainty cited in BSL for these correlations.
The disturbing thing about that graph in BSL is :

1. The line of the graph is thick, leading to inaccuracies
2. At Re = 60,000 the line is actually below 0.003, which is another inaccuracy. At Re = 10,000 also, its below 0.004 - that means the Nusselt numbers are smaller than calculated - that would have been comforting. But the problem being that the Nu by Seider-Tate comes to be bigger. If it came to be smaller, I could have thought of it as the inaccuracy in the line of the graph (and my vision).

In my judgement, you're splitting hairs, and asking for more accuracy from the correlations than is realistic. Furthermore, remember that the uncertainty in the outside heat transfer coefficient is much larger than this, so why are you torturing yourself in pursuit of just a few of percent more accuracy.

-------------------------------------------------------------------------------------

Also!

Since I have temperature based polynomials for the viscosity of the gas, I could as well include the viscosity factor in the calculations right?

viscosity factor = (mu_bulk/mu_boundary_layer)

Correct?
Yes. But, check BSL's description to be sure.
Here, the temperature of the bulk gas is the T_gas_estimated, and the denominator is the INNER film temperature right? I am just going to include the (viscosity factor)^0.14 in the Nusselt number equation.

And which would be a better pick, Seider-Tate or BSL? If Sieder-Tate is more accurate, I want to use BSL for Nusselt numbers up to the value of 10,000 and then use Sedier-Tate from there on. But which is more accurate in your opinion?
In my opinion, again, you're splitting hairs. The correlation in BSL appears in many other books, and BSL indicate that it is based on Seider and Tate's data. They even give an equation with a 0.027 instead of 0.026. Any of these choices that you describe is adequate, and they all have about the same degree of accuracy.

Several posts ago, I asked you to consider applying the flat plate approximation to the exhaust gas flow inside the tube (with the leading edge at the exit of the muffler) to see how the value of the heat transfer coefficient compares. This is because the Seider -Tate and BSL correlations for internal flow are based on fully developed velocity profiles in the pipe, while, in your case, the region of interest is in the hydrodynamic entrance region of the pipe, where the velocity profile is still developing. Have you had a chance to check this out yet?

Chet

Okay I will go with BSL. It's just that I am doing something like this for the first time. I usually assume physics has exact equations for given situations. I will be back if I have questions.

Thanks Chet.

Jay_ said:
Okay I will go with BSL. It's just that I am doing something like this for the first time. I usually assume physics has exact equations for given situations. I will be back if I have questions.

Thanks Chet.
Welcome to the world of experimental correlations of data.

Chet

Hey Chet. This is good.

However, my professor has asked me to include the coolant heat transfer estimation into the project too "if I can".

Now, I want to put some effort into it. I am using an OBD data logger and so I am going to have the coolant temperature with me directly. So, the only things I really want would be :

1. Coolant mass flow rate
2. Coolant specific heat capacity

Have you any idea of equations on these? I searched Perry, and the Graduate Naval school document they don't have specific heat capacity of Ethylene glycol solution as a polynomial in temperature. But I could use this and create a function in MATLAB :

I am going to assume a 50%-50% solution (so 4th column), I think that would be good. But let me know if I am wrong.

--------

How would I estimate the flow rate? I read a thread here in physics forums, and also another site. I don't find anything conclusive.

See following Engineering Toolbox link for properties of antifreeze:http://www.engineeringtoolbox.com/ethylene-glycol-d_146.html

Also see:

A typical coolant circulation rate is 5 gpm, but, of course, it depends on the engine speed.

Here's a Physics Forums thread on coolant flow rate (lots of good meaty info for you): https://www.physicsforums.com/showthread.php?t=566125

Chet

A typical coolant circulation rate is 5 gpm, but, of course, it depends on the engine speed.

I am going to be acquiring the engine rpm from the OBD data logger as well.

Since, the OBD data logger gives me both the engine rpm as well as the coolant temperature, I don't need to find the heat transfer coefficient or all the other things. Because I have the temperature of the coolant, and I need the energy of the coolant. So its directly plugging it into the equation for rate of heat.

I can make a function for the specific heat capacity of the coolant from those links. So, if I have the mass flow rate, I have everything I need.

So, what would the exact relation between the coolant circulation rate and engine rpm be? The link doesn't give me that even if it gives me a rule of thumb in the second post (what's the source?).

Jay_ said:
I am going to be acquiring the engine rpm from the OBD data logger as well.

Since, the OBD data logger gives me both the engine rpm as well as the coolant temperature, I don't need to find the heat transfer coefficient or all the other things. Because I have the temperature of the coolant, and I need the energy of the coolant. So its directly plugging it into the equation for rate of heat.

I can make a function for the specific heat capacity of the coolant from those links. So, if I have the mass flow rate, I have everything I need.

So, what would the exact relation between the coolant circulation rate and engine rpm be? The link doesn't give me that even if it gives me a rule of thumb in the second post (what's the source?).
I didn't keep track of the source. I just Googled Coolant Flow Rate, and this was one of the choices.

If one is serious about getting the coolant circulation rate, one needs to know the so-called pump characteristic. The water pump in a car is a centrifugal pump, and the characteristic tells you the volume flow rate through the pump as a function of the pressure buildup across the pump and the rotation speed. This information usually is supplied by the pump manufacturer.

Is there any way you can just measure the water flow rate in the inlet and outlet lines to the radiator?

Chet

Chet

No, as of now its too late to get into acquiring those data. I guess I will tell him there is nothing certain I could find on the flow rate of the coolant.

If you had the pump characteristic of your particular water pump (maybe it's available on line) and you could measure the pressures into and out of the radiator, you could get the flow rate. However, I guess there's not enough time to do this.

Chet

There is time to do calculations based on characteristics we acquire from manuals, or standard values. There just isn't time to buy any new instrumentation systems, and program them.

The car I am using now is a Ford F-150. The reason my professor wants the coolant energy is to use it as a standard to compare if the model got the exhaust gas energy within acceptable values.

A lot of literature gives us the ratio of the exhaust gas energy to the coolant energy. So, even if we have rough values of the exhaust gas energy or coolant energy for a vehicle like the Ford F-150 we can compare those values to see if the model is right.

Hi Chestermiller, something terrible has happened. We aren't using the temperature sensor, but only the OBD data logger and we are acquiring the following parameters directly - vehicle speed, coolant temperature, engine rpm, throttle position and air flow into the tank. I feel terrible for wasting your time.

So, there is no exhaust temperature! And today we tried fitting the temperature sensor under the exhaust pipe and my professor just said, we don't need it. This has really upset me, because I feel he should have let me know about this as I was putting efforts on it.

So basically all my efforts in programming my sensor for the past 2 months, and this whole discussion for the past 7 months are as good as nothing (but it was a good learning I had, thank you).

Since, I do need the exhaust temperature OR the coolant flow rate. I would like to ask you if there is any way to model the exhaust temperature FROM the coolant temperature, or get to the coolant flow rate.

Data I have logged (inputs) :
1. Vehicle speed
2. Coolant temperature
3. Engine rpm
4. Air flow
5. Throttle position

Now, we are using a Ford F-150 Triton V8 engine, model 2002. I will try finding the exact pump or part you need the specs for. But the above 5 are the only changing parameters I have. The logger only allows for 5 parameters to be measured at a time. I will list other parameters, tell me if they are important to our calculations. I felt the above 5 are important.

Assuming we have the above 5 logged, and also using certain unchanging parameters what is the best way to model this? Even if we just found coolant flow rate, OR temperature of gas, we are fine. Any one from the above 5.

Last edited:
Jay_ said:
I need to work quickly. Because I have to complete it by the end of this month.

I found this online :
http://www.fordservicecontent.com/F...ner's-Manual-First-Print_om_en-us_09_2013.pdf

But it says nothing about the radiator hose or pump. I can't find it in the index.
Hi Jay.

This is really bad news. I don't know what your professor's ultimate objective is, but I am assuming it is to determine how much energy is available from the fuel air mixture once you subtract the energy exiting the exhaust and the cooling system (radiator). Of course, not all this energy is available as drive power, because there are losses due to friction, running the fuel pump, running the water pump, running the air conditioner, running the oil pump, etc.

As we said, you know the exhaust flow rate and composition, but not the exhaust temperature. The problem is, you can't determine the energy exiting the exhaust without knowing the exhaust temperature.

As far as the cooling system is concerned, you could be in a little better shape if you could estimate the coolant flow rate. When you say that you know the coolant temperature, I am assuming you know it at the entrance to the radiator. Any chance you also know it at the exit? As far as the coolant flow rate is concerned as a function of the engine speed, the reference you sent (owner's manual) is of no use. But, you may be able to find more information in the Shop Manual. Shop manuals are available on line and also may be in the library. There is also the effect of the thermostat to consider. The thermostat, I think, controls the fraction of the coolant the bypasses the radiator, and is keyed to the coolant temperature coming out of the water pump.

Chet

This is really bad news. I don't know what your professor's ultimate objective is, but I am assuming it is to determine how much energy is available from the fuel air mixture once you subtract the energy exiting the exhaust and the cooling system (radiator)

Yes. I need you through this sir. The objective of this project was to estimate the energy that is wasted in the form of heat through the coolant and the exhaust. Initially, my plan was to work with the exhaust energy and since literature tells me the ratio of energy wasted between the two, I could estimate the energy wasted as heat through the coolant.

Now I checked my data logs the coolant temperature seems to just vary mildly - from 84 deg C to 91 deg C, over a wide range of speeds (0 to 120 kph). Given that this is roughly constant, I am assuming my logger is actually measuring the cooler temperature.

Now, if we could model the hotter temperature as a function of the above 5 inputs, and also the flow rate as a function of the engine rpm, or get these from literature, we will be done.

My first thought is, since the cooling in the radiator hose is radiative, could the Stefan-Boltzmann law come to help in estimating the temperature at the other end?

Jay_ said:
Yes. I need you through this sir. The objective of this project was to estimate the energy that is wasted in the form of heat through the coolant and the exhaust. Initially, my plan was to work with the exhaust energy and since literature tells me the ratio of energy wasted between the two, I could estimate the energy wasted as heat through the coolant.

Now I checked my data logs the coolant temperature seems to just vary mildly - from 84 deg C to 91 deg C, over a wide range of speeds (0 to 120 kph). Given that this is roughly constant, I am assuming my logger is actually measuring the cooler temperature.

Yes. That's the outlet temperature from the radiator.
Now, if we could model the hotter temperature as a function of the above 5 inputs, and also the flow rate as a function of the engine rpm, or get these from literature, we will be done.

My first thought is, since the cooling in the radiator hose is radiative, could the Stefan-Boltzmann law come to help in estimating the temperature at the other end?
No. Even though it's called a radiator, the mode of heat transfer is convective.

Chet

The fan gives it a forced cooling though right?

How are we modeling it? Is it even possible with the 5 parameters I listed? Let me know if I have to find any particulars about the car.

Hey Chet,

I got an idea. Since my professor wants to know if the values I get are real, and literature tells me that around 33% of the energy is lost through the exhaust, I am just going to compare the value I get of the exhaust to the total energy based on the calorific value of the fuel burned.

I have the distance traveled in my logger. I have the mileage of the car for a given drive cycle. I can thus find out how much fuel gallons I used, and thus the grams (from the density). Based on that and the calorific value, I can find how much energy was used in total.

Then I have to show that the energy given off from my model is roughly 33% of this total, which is basic math. Is this reasoning sound? If it is, I have to speak to him about it, because I would prefer that all the efforts of the past many months don't go in vain. I also have a friend who has a car, and he is willing to help me with placing the sensor under the car.

Many cars don't have enough ground clearance, the Ford F-150 we used earlier had a exhaust pipe arrangement that was difficult to have a sensor on, there was no position for it, and also the pipe split as two at (beginning point) where we wanted to set it up. Now I am using a Nissan Maxima, and hopefully it gets done!

Jay_ said:
Hey Chet,

I got an idea. Since my professor wants to know if the values I get are real, and literature tells me that around 33% of the energy is lost through the exhaust, I am just going to compare the value I get of the exhaust to the total energy based on the calorific value of the fuel burned.

I have the distance traveled in my logger. I have the mileage of the car for a given drive cycle. I can thus find out how much fuel gallons I used, and thus the grams (from the density). Based on that and the calorific value, I can find how much energy was used in total.

Then I have to show that the energy given off from my model is roughly 33% of this total, which is basic math. Is this reasoning sound? If it is, I have to speak to him about it, because I would prefer that all the efforts of the past many months don't go in vain. I also have a friend who has a car, and he is willing to help me with placing the sensor under the car.

Many cars don't have enough ground clearance, the Ford F-150 we used earlier had a exhaust pipe arrangement that was difficult to have a sensor on, there was no position for it, and also the pipe split as two at (beginning point) where we wanted to set it up. Now I am using a Nissan Maxima, and hopefully it gets done!

I'm a little confused. The sensor is back in the picture again?

Chet

Hi Chet,

Yes. I couldn't let all that work go waste. So I used my friend's car and we got some temperature data of the pipe. We had to do a city drive cycle and also a highway drive cycle.

The temperature sensor stopped sending data in the highway for some reason, so I only got some of it. The thing is I needed to use the temperature sensor, because I have already typed 20 pages on the report over the model and the sensor.

But since I have the 5 data from the OBD data logger (engine speed, coolant temperature, vehicle speed, air flow, and throttle). We need to model the coolant quickly and use the coolant temperature data on that. Even a rough estimate is good for modeling the flow rate and the cold-side temperature.

Okay. I would but the units on the y-axis are unclear. Also it says cm^3/cycl would that mean for a 6 cylinder, I would have to times the value with 6.

I tried searching for another graph, and I feel unsettled whenever I come across information that contradicts. Look at the one I found, it seems to show that the flow rate increases with engine rpm almost linearly. Do these contradict or have I misunderstood?

If they do, which would be the better one to go with?

http://files.engineering.com/getfil...34-bc19-41780227b743&file=cooling_montage.jpg This one is for a V8 though.

The y-axis in the Howarth plot is dimensionless, and is the ratio of the radiator heat load to the brake horsepower at spec RPM. Consider this reference:

It has info similar to the Howarth plot, saying that y is about equal to 1.0, as a rule of thumb.

The plot is suggesting that the heat load is nearly constant over a wide range of engine speeds. This implies that, as the engine speed increases (and as the coolant flow rate increases), the temperature drop in the radiator decreases nearly inversely. Your other graph shows the coolant flow rate through the radiator increasing with engine speed. I would assume that the coolant flow rate is nearly directly proportional to the engine speed, as suggested in your other plot.

Chet

So, the graph from the physicsforum page isn't useful unless I know the bhp at each rpm right? Because that is the only way I could calculate the flowrate.

I am hesitating to use the other graph because its for a V8. But if I find nothing else, that is what I would have to go with given that I have 8 days left.

Hey Chet,

Let me know if the following is a correct way to go:

The graph in the other physicsforum thread gives me the decimal number to multiply with the horsepower right? Now I am using 2007 model, so that is 6th generation and this graph below gives me the horsepower with respect to rpm. But my engine size is bigger 3.5 L would it make a big difference?
http://home.comcast.net/~stevtecv6/dynos/NHT_30V6_HP_MD_j30eststock.jpg has

Last edited by a moderator:
Hey Chet,

Let me know if the following is a correct way to go:

The graph in the other physicsforum thread gives me the decimal number to multiply with the horsepower right? Now I am using 2007 model, so that is 6th generation and this graph below gives me the horsepower with respect to rpm. But my engine size is bigger 3.5 L would it make a big difference?

has the wheel horsepower I believe.

So the break horsepower would be 15% greater (or I might take 22% from the middle of 20-25% in the note below) from this link :

I go to Link 1, but to convert the wheel horsepower to brake horsepower, I go to Link 2. I then multiply it by the corresponding number in the ordinate of the graph in the physicsforums thread.

Is that reasoning good?

Last edited by a moderator:

• Thermodynamics
Replies
2
Views
1K
• Thermodynamics
Replies
4
Views
15K
• Introductory Physics Homework Help
Replies
19
Views
2K
• Aerospace Engineering
Replies
10
Views
1K
• General Engineering
Replies
21
Views
2K
• Mechanical Engineering
Replies
4
Views
1K
• Thermodynamics
Replies
14
Views
2K
• Classical Physics
Replies
18
Views
1K
• General Engineering
Replies
11
Views
3K
• Mechanical Engineering
Replies
3
Views
615