Impact force on suspended concrete slab from sludge dump

[hetgen]

Please engineering gurus I need help!

How would one conservatively calculate the impact force from 30 cu.m (~1000ft3) sludge dump to a suspended concrete slab? See attached diagram for dimensions.

Density of the sludge is 1200kg/cu.m (~75lb/ft3) and its dynamic viscosity is very much close to water.

I won’t dare to post my dreadful trials as I wasn’t even close to estimate contact area the sludge at time of impact.

Regards

 

[Denial]

My trusty old friend, First Principles, suggests applying Newton's second law: force = rate of change of momentum.

Applied to an apple, this becomes F=ma.

Applied to a stream of fluid, it becomes F=dQv
where d is the fluid's mass density, Q is the volume flow rate of the fluid, and v is the fluid's velocity when it hits the slab (after free-falling whatever distance).

If the fluid does not contain any lumps, then I would not use the term "impact" to describe what is going on. It is more an exercise in fluid dynamics.

But none of this is my usual area of work, and there might well be other phenomena involved as well.

 

[hetgen]

Thanks Denial,

The sludge is from a mining process and I was told that it doesn’t contain sizeable solid mass, thus there is no much impact happening; Inanycase, it wont matter if we going back to first principle of conservation of momentom and energy.

If we ignore effect of friction, viscosity and things that I don’t know, to apply first principle one need to know
• Velocity before impact
Using conservation of enrgy, velocity of free falling object before impact u1=sqrt(2*g*h)
• Velocity after impact
The fluid will bounce upward, at what velocity? if we ignore this velocity aren’t we under estimating the change in momentum?
Newton’s 2nd law of conservation of momentum (force = rate of change of momentum) F=Q * density (u2 –u1).
• Area of flow before the sludge hit the slab.
Will it be valid to use law of continuity Q=A1u1. This area is required as force with no area of application doesn’t help.

 

[a2mfk]

Maybe someone in one of the other forums can be more help in determining this type of force- maybe a coastal engineer or mechanical engineer that deals with fluid dynamics?

 

[Denial]

As I implied, I am no fluid mechanicist. However if I was trying to "get a handle" on this problem I would apply the formula I gave above.

» You know d.
» I would use sqrt(2gh) for v. (I cannot see any significant rebound effect happening. Any sludge that wants to bounce will have to do so into the face of further down-falling sludge. But if you are worried about this make some sort of allowance — say a bounce speed of half the impact speed.)
» You know the total quantity dumped. Get the overall time for the dumping operation, and you have the average dumping rate. For Q you need the peak dumping rate. Two times the average? Five times the average? Take a look at the operation and see how "bursty" it might be. Then throw in a factor of safety.
» I am not sure why you are getting worried about the "area of flow". By my equation this will not affect the total force: it will only affect the area over which the force is applied.
» Don't forget that this "dumping" force is additive to the static load resulting from the sludge that has already arrived. Thus the maximum total force MIGHT happen later than the time of peak dumping rate.

HTH