Fluid Flow from gravity - Sanity Check 1

[NeedAHoliday]

Dear All,

I need a sanity check on some number crunching I have done.

I have a make-up water tank that is at atmospheric pressure with a water column height of 3.1m with the outlet nozzle of tank to scrubber inlet vessel of 2m (therefore conservative column height is 2m of available head).

There will be approx 5m of piping with 4 off 90degree elbows and a level float valve within a scrubber sump to act as flow control valve.

I need to have a flow of 5.3l/sec to accomodate the discharge flow rate and maintain a constant scrubber sump height. The sump will be under negative pressure of about 1000 Pa at water discharge point (i.e. P2 = -1000).

Using Bernoulli's equation and negating pump energy inputs I end up with:

P1/rho + V1^2/2g + Z1 = P2/rho + V2^2/2g + Z2 + hF + hM

where P = pressure, V = vel, g = gravity, Z = height, hF = friction losses in pipe and hM = mechanical losses due to fittings

Now P1 and V1 = 0 as at atmospheric in a static tank. deltaP = -1000Pa, and delta Z = 2.0m

The procedure I have taken is to solve the required velocity to ensure that my total dynamic head exceeds friction and fitting losses. I have done this by solving Bernoulli's equation (as written above) while simultaneously recalculating my frictional losses with varying flow velocity (by Darcy-Weisback and Colebrook's formula) until I get a slightly higher total dynamic head to friction losses, this gave me a velocity of 2.1m/s which equates to a pipe size of 50NB sch 40, which is my limiting pipe size.

Alternatively if I negate all regain effects, which is the negative pressure in column (i.e. deltaP = 0) then I would have around a 80NB sch 40 pipe with a vel of 1.111m/s

I would like to know if my method is sufficient or should I look at doing it in a more rigorous way and which value for my line size is the more realistic.

All inputs appreciated. If anyone can actually do a check on my numbers that would be a great help.

Cheers.

P.S. Hope my post makes sense to you all, if any clarification required feel free to beat me over the head for not giving a clear posting, and I will supply any additional information!!!

 

[25362]

Without making calculations, I don't see why neglecting the 1000 Pa advantage (~0.1 m water head) should make a marked difference. As I see it the first 50NB option should be able to overcome the line (+fittings) friction drop with enough hydraulic head left for the LLCV to operate even without the so-called "regain". Am I right ?

 

[katmar]

As 25362 has pointed out, the "vacuum" in the column contributes only 5% of the head available. I would neglect it in any calculation.

By my calculation the pressure drop through a 50NB pipe and 4 off elbows would be almost exactly 2m of water head. There would be nothing left for the float level valve.

In my experience this type of valve requires quite a large head. They are made with small orifices so that it is relatively easy for the float and lever arm to shut the valve off tightly.

You need to find out from the valve supplier what pressure drop is required to deliver 5.3 liter/second through the valve, and then size the pipe and fittings based on the residual pressure drop.

regards
Katmar

 

[25362]

Of course if the make-up water tank head of 3.1 m can be ensured the picture changes. Right ?

 

[NeedAHoliday]

katmar,

Thank you, I felt I was missing something and the float valve dP seems to be what was playing on the back of my mind, will do some more digging.

25362: To both your response Yes and yes. I am actually already investigating what the guaranteed tank operating level will be.

Cheers.