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# Pipe Flow (Sudden Contraction)3

## Pipe Flow (Sudden Contraction)

(OP)
Hi all!  I have a problem with my calculations.  A customer has a boiler operating @ 1385 psi.  For blowdown (to atmospheric tank) they intend to open a valve on a line attached to the boiler (connected to blowdown tank) and I'm trying to calculate the maximum flow possible through the 1.5" line.

I know that volumetric flow = velocity * area, but I'm unsure how to calculate either the velocity or the volumetric flow.  Should I use an orifice calculation or would bernoulli's equation suit me better.  I have calculated the flow possible by using an orifice calc., but am skeptical (it seems really high).

Dan
Replies continue below

### RE: Pipe Flow (Sudden Contraction)

I'd reckon the flow ought to be very high with 1385 psi driving it!  I ran a quick calculation in Crane Companion software.  If you have 1385 psia saturated steam at the inlet, and have a 10' long 1½" pipe discharging to atmosphere, the mass flow rate works out to ~103,000 lb/hr.  Increasing the line length to 100' still flowed ~54,000 lb/hr.  Is this in the ballpark of your calculations?

### RE: Pipe Flow (Sudden Contraction)

(OP)
We are to assume the length of the pipe @ 100 ft for bidding. Also, I believe the exiting fluid is saturated liquid (at least initially).  The pressure drop along the way to the blowdown tank is going to make the liquid flash, but I really haven't taken that into account.  I was using just an orifice calculation and was getting ~640,000 lb/hr flow.  This seems excessive to me even with 1385 psi behind it.  Am I missing something?

Dan

### RE: Pipe Flow (Sudden Contraction)

I did a quick look using Crane.  Assuming 100 feet of 1.5" pipe with different schedules I got the following:

sch 160, 190,000 lb/hr
sch 80, 255,000 lb/hr
sch 40, 310,000 lb/hr

Basically took saturated water at 1385 psig and ignored the flashing that will occur which will actually choke the flow through the pipe to less than this, likely quite a bit less.  I didn't include an exit loss (K=1), that would reduce these a bit but I don't get anywhere near 640,000 lb/hr.

How are you doing this as an orifice calculation?

I'd take a look at calculating the total K factor of the 1.5" line, convert this back to a Cv per the method in Crane and then calcuate how much saturated water I could push through the 'valve' (Fisher catalog will show you the calc).  If you don't have that, let me know and I can do a quick check for you.

It's rough but the only better way is to do a 2 phase flashing flow calculation down the 1.5" line.  I'm not sure Pipephase would handle it, my experience is that it doesn't like very high velocities.  SimSci also has a similar program for flare systems that do handle high velocities, multiphase mixture but it is likely overkill for what you need.

You could try sweet talking Pete, I know he has a copy of Pipephase

### RE: Pipe Flow (Sudden Contraction)

(OP)
Thanks guys for the response, I think I'm getting a better handle on the situation.  I believe I was wrong to even think of doing an orifice calculation.  I actually found an example problem in one of my old textbooks.

When I followed the text's example (it uses the Bernoulli equation with constant density), I came up with a flow of 250,000 lbm/hr which is similar  to that which TD2K came up with for sch. 80 pipe.

When I recalculated the equation and factored in the downstream density, I got a flow of 171,000 lbm/hr which is similar to the flow calculated by using jmw's compressible flow calculator.

I assume that the flow I calculated while taking into accound the downstream density is more accurate... is this true?

Thanks!!!

Dan

### RE: Pipe Flow (Sudden Contraction)

Dannyo, I took a 100 feet of sch 80 pipe and added in the entrance and exit losses for a total K of about 18.1.

That's equivalent to a Cv of about 15.8.

Using the approach in Fisher and assuming the pipe is 'similar' to a full port ball valve with respect to a pressure recovery factor (Km = 0.3), I get a flow through the line of about 56,000 lb/hr or about 20% of my previous estimate for only liquid.

At the pipe outlet, over 55% of the water has flashed to steam and on a volumetric basis, over 99.9% is flash steam.  I'd expect therefore most of the pressure drop to occur over the last portion of pipe as more water flashes to steam, the flash steam already existing expands due to the reduction in pressure.  The result is you need more and more pressure drop to move the total fluid through each additional foot of pipe.

This is obviously a rough calc and full of possible points to 'discuss' but it's pretty obvious that the effect of the flashing steam is significant.

### RE: Pipe Flow (Sudden Contraction)

i ran a two phase flow similator under adiabatic conditions an calculated 75,000 lbs/hr for 100' of 1.61 inch id pipe.  The outlet velocity was exceeding the speed of sound, so i reduced the flowrate to 70,000 lbs/hr to keep velocity under the 1660 feet/second speed of sound in steam.  At these conditions, the steam would be at over 400 psi at the end of the pipe.

### RE: Pipe Flow (Sudden Contraction)

In this valve sizing problem you are talking about boiler WATER, aren't you?  The boiler blowdown water is likely cooled against feed water, so it should be highly sub-cooled, at least upstream of the valve.

Whether for continuous or intermittent boiler water blowdown, you should have no problem finding manufacturers with standard products and info...

Further comments on code requirements here will be interesting .. it is such a common item ... will flashing occur at valve outlet (likely), in piping downstream of the valve or will there be an orifice immediately upstream of the flash tank to prevent flashing near the valve ...

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