Calculate Air Flow Force for Piping System Setup

[bigdads]

See attachment for piping system setup.

Question: How much FORCE will the block feel from the air flowing through the two holes in the lower pipe?

I have no idea how to calculate this. Does Bernoulli's equation apply anywhere here?

 

[Shawnzyoo]

it looks just like a problem straight out of my fluid mechanics textbook
bernoulli's should apply
and conservation of masses
mass of all inputs - mass of output = total mass change in the system
and for this system
mass in = mass out

 

[bigdads]

So you have 4 inlets & 1 outlet...

Conservation of mass??:

A1v1+A2v2+A3v3+A4v4 = A5v5

unknowns: v1, v2, v3, v4

A=area
v=velocity

Bernoulli??:

P1+P2+P3+P4+(1/2)p(v1^2+v2^2+v3^2+v4^2)+pg(z1+z2+z3+z4) = P5+(1/2)p(v5^2)+pg(z5)

P=pressure
v = velocity
p = density
g = acceleration due to gravity
z = height

Assumptions: P1=P2=P3=P4=atmospheric pressure

unknowns: v1, v2, v3, v4

2 equations, 4 unknowns...How can this be solved?

How can I use this to get the force on the block?

 

[FredGarvin]

You're not going to be able to cover the entire network in one swoop. Start at the node where the two pipes meet and apply the continuity equation: Q = Q_1 + Q_2 where the total flow is the flow from the fan. That will give you the two flow rates (a function of the diameters). Now that you have the flow rate at that node, you can now go to Bernoulli and continue back up the pipe to calculate the pressure drop around those holes.

Just out of curiosity, when you say "force on the block" you are referring to a lower pressure that will (I hate to use this term) "suck" on the block? In other words, you want to know if you'll have enough flow to pick up the block?

 

[bigdads]

Just out of curiosity, when you say "force on the block" you are referring to a lower pressure that will (I hate to use this term) "suck" on the block? In other words, you want to know if you'll have enough flow to pick up the block?

Yes