Vertical Vessel Orifice Drain Impacting Inclined Surface Force Calculation 1

[Bill Blarney]

Have 100 feet liquid level vertical vessel discharging water through large diameter orifice by gravity.
The draining orifice jet impinges on an inclined deflector 12 feet below the 60-inch discharge valve.

Used Bernoulli's equation for the initial fully-open valve flow:

Q(0) = 0.5 [√ (2 · (32.2) ·100)] π ·2.5 2 = 0.5 · (80.2) · (19.6) = 788 ft3/sec at 40fps
√ (1 – 2.5 4 / 14.3 4) (0.9997)

Then increased velocity for the freefall drop and decreased the diameter for conservation of momentum,
and get ~ 51 fps impacting a 53-inch diameter circle, onto a steel-shielded 45º concrete impact surface.
The reaction will equal the force of impact vertically, and equally horizontally, for 1.41 times impact.

That should be everything I need, but I'm not finding the equation! I know that's stupid but I lent my
Chung, Comp Fluid Dynamics to another engineer and he departed with it. I used to know this by heart.
Anyone have an online link, or care to post the formula(s)? If I get it wrong, things will go break.

 

[ione]

F=rho * Q * delta(v)

 

[LittleInch]

I wasn't sure about the data, but looking at this

https://www.engineeringtoolbox.com/flow-liquid-water-tank-d_1753.html

It seems to be correct, but only when you consider the hole to be a sharp edge orifice. A smoother one will generate even large flow by a factor of about 1.5.

But what is this thing? A 30m high vessel with a 60" valve?

Why do you think the diameter of the plate reduces? This flow will tend to diverge not converge?

If this is supposed to impact a plate which is simply angled at 45 degrees there is going to be some force there.

40 - 50 tonnes force is my OOM estimate.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[HTURKAK]

The formula which mr ione (Mechanical)has written is correct but, a contraction will develop at exit (VENA CONTRACTA )

and the relevant factors Cc,Cv,Cd can be found at any fluid mechanics book. Assuming the 60-inch discharge valve (the diameter could be typing mistake??) is connected to vessel with a flanged nozzle,in this case the exit can be assumed mouth piece.I am retired engineer and have free time . I performed the calculation with hand but did not check for calculation errors..

 

[Bill Blarney]

Thanks all. Yes this is a coker vessel discharging through a 60-inch knife valve.
Pet coke slurry is anywhere from 0.9 specific gravity up to 1.7 specific gravity,
but that just factors out as the FOS in design, easier to use 62.4 for the calcs.
I used Cd=0.5 instead of Cd=0.8 for initial report years ago, that's lost in time.
Fv=rhoQV was the formula I was looking for, HTurkak kindly confirmed my method in
doing all the calcs, I appreciate that beyond what words can express. Thanks again.