recycle temperature 1

[ratash]

I have a pump system, which may go into 100% recycle for many hours. I would like to calculate what the tank temperature will be after 10 hours. At time = 0 T= 120 F, tank volume = 5000 gallon, cp = 1.0 Btu/lb/F, the recycle flowrate = 5 gpm.

 

[quark]

A simple method is to calculate the difference of BHP and WHP and calculating the temperature rise as if you have placed a heater of this capacity into the tank. Temperature rise will be lower for an uninsulated system.

Calculate WHP by the formula 8.33xHxQxSG/33000, H is in feet and Q is in gpm

Check

http://www.mcnallyinstitute.com/01-html/1-04.html

thread407-96694
thread124-102433

and many more threads on this site.

 

[ratash]

Thank you so much for the tips and the site. However, I need differential equations to solve for temperature at time n. There is a temperature rise the minute I pump, but as I keep circulating the liquid, its temperature will keep going up.

 

[Powerman81]

temprature keeps going up due to the heat input from pump motor. If you need a DQ to calculate the temprature at time t, you need to utalize the general energy equation P*Cp*dT/dt= q*V where:
P: fluid density
q: Heat rate (input)per a volumatric flow rate
V: volume
Cp: specific heat

Try it

 

[ratash]

Thanks. I need to intergrate with respect to time, which shows up on the right side of your equation. I am totally rusty on setting up differential equations. Could you help me please?
At time = 0, cp = 1btu/lb/F, m = lb/hr, volume = 6000 ft3
energy balance is: in-out= accumulation, so:
Lb/hr*btu/lb/F*(T2-T1)= IN = 1000*(1)*(120-120)= 0
Out = -(1000*(1)*(T2-120))= d(mcpdelta T)/dt
= m dT/dt +(T-120)dm/dt => dm/dt = 0
Material balance:
0-1000 = 0 => dm/dt = -1000 Past this step I am lost, but I give it a try:
1000*(T-120)= mdT/dt = 6000*62.4*dT/dt+6000*62.4*Tdm/dt
1000ln(T-120) = 6000*62.4*ln(T-120), I am lost.

 

[vpl]

There is a temperature rise the minute I pump, but as I keep circulating the liquid, its temperature will keep going up.

This depends. If the recycle line is very short and goes directly from the discharge to the suction, then, yes, it will keep going up and up. On the other hand, if the recycle line involves the pump pulling from the bottom of a tank with a discharge line going back to the top of a tank, with significant lengths of piping between and a large volume of water, the temperature may not go up that much at all. You can still use the general equation given by Powerman81, but your values will change.

As an input point, the Nuclear Regulatory Commission issued guidance back in the late 80's about operation of pumps required to mitigate accidents if they went on a long-term recycle. Two specific guidance documents, available on the NRC website (

http://www.nrc.gov)

are Information Notice 87-59 and Bulletin 88-04. In general, utilities provided responses back on the Bulletin indicating that a recycle flow rate between 10 and 25% of total flow was adequate to ensure continued pump operation without overheating. The differences arose from the length of pipe and the recycle path. (To find the Informatin Notice and Bulletin, select Electronic Reading Room from the list of the left side of the page. Then select Collections of Documents by Type and then Generic Communications.)

Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[ratash]

Thanks. Any idea on solving the differential equations for me?

 

[Powerman81]

something is wrong with the DQ I provided you above. I will get back to you ASAP

 

[quark]

Don't complicate the calculation. Suppose, you run the pump for one minute and the difference of bhp and whp is 1, 5 gallons of water gets in 42.4 btus of heat. This will, subsequently, heat up 4950 gallons of water in the tank.

In a simple way, you can calculate 42.4 btus of heat rising the temperature of 5000 gallons of water. The temperature increase will be 42.4/(8.33*5000)= 0.001F

Now, run the pump for 10 minutes and the temperature rise will be 0.01F.

Your final simple formula can be written as [Δ]T = 0.001*(BHP-WHP)*t (where t is minutes of pump running)

 

[speco]

Quark,

A star for you for recognizing that "it's just not that complicated." Who needs differential equations for a straight line anyway?

Speco

 

[quark]

speco,

Thanks for the undeserved star. As you exactly pointed out, this is a straight line function.

ratash,

Q*dt = mCpdT should solve your requirement. The time rate of change of heat input is constant and it comes out of the integrand. Finally, it boils down to [Δ]T = Q*t/(mCp) and this is what my simplified equation gives you.

 

[ratash]

Thanks.

 

[gmax137]

quark -
Your formulation begins by subtacting the WHP from the BHP, and then uses the remainder as the heat input to the fluid. I have seen this done before, and I always wondered about it. If all of the flow is recirculated to the source tank, shouldn't the entire BHP go into heating the fluid? It seems like the WHP goes into friction along the pipe (and hence heat) and any "left over" pressure energy is dissipated in the tank.

Thanks

 

[quark]

That is a nice question and unfortunately I don't have a clear answer. This topic was discussed couple of times in previous threads without solid conclusion.

Obviously, the upper limit for heat up calculation is BHP and lower limit is (BHP-WHP). ASHRAE suggests using BHP for recirculation systems incase of heat load calculations.

However, this is quite conservative approach. For example, (1) The inefficiency of the pump and the friction at the pipe walls do impart heating to the fluid. However, WHP is not totally offset by friction. The liquid does have kinetic energy which, ultimately, gets dissipated in the tank.
(2) WHP should take care of the static head of the fluid.
(3)Some portion of energy is being used to displace the air from the tank.
(4)Heat is lost to the atmosphere from piping and tank.

So, I think this is a risk based approach. Do you have any comments on this?

Regards,

 

[gmax137]

So, I guess how you do your calculation depends on the situation, and what you're trying to achieve. Now there's a surprise

If your situation is big pumps in a small system, and a few extra degrees (or Btu/lb) are important, then maybe considering all of the BHP going into heat might be an appropriate approach. If, on the other hand, the effect is small relative to other assumptions or approximations you're making, then maybe you can let it go...

thanks for listening