# How far water flows in a tilted oven before evaporating?

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1. Feb 11, 2015

### crclayton

If I throw 10 gallons/minute of cold water for 4 days into an oven that's 300°C Celcius and 300ft long sloped at an angle of 10°, how far would the water make it down the oven before completely evaporating?

Even if you can't solve this directly, I'd love some advice or recommendations of how to approach the problem. I'm an EE student on an internship and this is totally out of my area of expertise.

2. Feb 11, 2015

### Staff: Mentor

Welcome to the PF.

Is this a schoolwork problem? If so, it needs to be posted in the Homework Help section of the PF, and you need to show some effort on the solution. What is the context of the question?

3. Feb 11, 2015

### crclayton

Thanks! No, it's not a homework problem, I'm on an internship working at a mill and have been asked to look into this. I've looked into Newton's cooling equation, hoping to get a value for the time it would take water to evaporate like so:

To = 10 degrees (cold water)
Tf = 100 degrees (evaporated water)
Ta = 300 degrees (ambiant temperature of oven)

T(t) = Ta + (To-Ta)e-kt = 100 = 300 - 290e-kt

But I'm having a hard time determining a value for K without a second reference. Any guidance or recommendations for how to solve this would be very welcomed.

4. Feb 11, 2015

### Staff: Mentor

The first thing to do is to focus on the hydrodynamics. What's the diameter of the pipe? If there were no heating, how much of the cross section would be filled? What is the method of heating in the oven?

Chet

5. Feb 11, 2015

### crclayton

It's 10 ft in diameter. As much as how much is pumped in would remain until boiled off. It's heated using natural gas and it's safe to assume that the pipe doesn't get cooled at all by the water and remains 300 degrees.

6. Feb 11, 2015

### Staff: Mentor

The pipe is heated from the outside? What about the air(?) inside the pipe. Where does it enter the pipe and where does it exit? The pressure is at 1 atm?

Chet

7. Feb 11, 2015

### Bystander

Looks like a cement kiln, and without some information about the burner, you're going to have a tough time figuring out how far down the tube the water might get before being carried back out the top end. Methinks you've been sent for a "left-handed pipe wrench," or "copper fallopian tubes," or some other rookie initiation equivalent.

8. Feb 11, 2015

### cjl

10 gallons of cold water a minute is going to have an incredibly large cooling effect, and this is not a trivial problem. There will be large internal temperature gradients, and the heat flux will be very large. I'm not convinced there's a reasonable analytic way to solve this.

9. Feb 11, 2015

### Bystander

3MW, a small cement kiln.

10. Feb 11, 2015

### cjl

Running some numbers here, you're putting in around 0.63 kg/s of water. Assuming the water is at 20C, it'll take 211kW to heat that water up to boiling, and another 1400kW or so to boil it off (it takes a very large amount of energy to vaporize water). Are you still sure that it's safe to assume the pipe doesn't get cooled at all?

Last edited: Feb 11, 2015
11. Feb 11, 2015

### Bystander

A 300 foot kiln? Thousand tons of material an hour being dried? We'll call it 360, 100 kg/s of presumably light minerals being dried, specific heat about a quarter that of water, another 5 MW on the burner. Residence time in the kiln? Fifteen minutes? Hour? Heat capacity of a "how many" hundred ton steel drum plus how many hundred tons of dried and drying product? Heat losses to atmosphere? Presumably the drum has some sort of lagging/insulation. Bulk materials processing is done in large numbers.
Are you being asked to come up with numbers to shove into process control algorithms to handle a "wet trainload" that comes into the plant?