Another Flow rate calculation?

[jscotty29]

The flow rate setting on my DCV is 30 GPM. The DCV controls a 4 stage telescoping cylinder. I'm trying to determine the discharge flow coming from the rod end when the cylinder is extending. i thought it was a simple velocity/cross sectional area. but i'm getting a discharge value that doesn't seem right to me. could someone please advise the correct formula?

here's what i did: v1=Q/A1(1st stage), Q2 = v1*A2(2nd stage), v2=Q2/A2(2nd Stage), Q3=v2*A3(3rd stage), v3=Q3/A3 (3rd stage), Q4=v3*A4 (Discharge Flow Rate).
by the time I get through all the area reduction ratios i barely have any flow coming out of the rod end.

 

[jistre]

Don't try to balance across each reduction in the system. Take the system as a whole to be your control boundary and write a mass balance equation for the whole thing. You'll have flow into the large end and flow out of the small end each given by Q=V*A. To complete the mass balance for the system, you have to also include a collection term on the exit side of the equation to account for the increasing volume in the arm as it telescopes out. Schematically, the equation should look like this:

flow entering the large end = flow exiting the small end + collection due to expansion of the arm.

 

[BigInch]

Formulas look OK. I'm not a telescope guy, but Q/A I can handle.

Cylinder n flowrate is,
Qn = Q1/A1 x An
Cylinder n Velocity is,
V = Q1/A1 and a constant

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[jistre]

Again, if I understood the problem correctly, we're still missing an important term. If the fluid travels through the arm, and the arm remains unchanged, then a simple Q=V*A analysis would work. Further, you could ignore all of the intermediate stages and focus on the inlet and outlet of the system provided the arm doesn't move, and the liquid is incompressible.

However, if I understand the situation, there is a telescoping cylinder involved. This cylinder has inlet and outlet ports at the large, "fixed" end and smaller "travelling" end, respectively. As the fluid is pumped into the large end, the fluid pressure acts on the telescoping arm, extending it, then ultimately flowing out of the small end. In this case, a term for the fluid that stays in the arm must be included in the analysis of any of the sections, as their volume is constantly changing as the system is running.

For instance, let's say you're pumping 1 cu. ft/sec of fluid through a cylinder. It is able to telescope, but it is all locked down, so it can't move. You pump the fluid through the cylinder in this case, and 1 cu ft goes in and 1 cu ft comes out per second. Now, the same system is running, and you release the locks. It just so happens that due to the telescoping action of the arm, the volume of the internal space increases by 1 cu. ft./second. Then, at the moment you release the locks on this system, fluid ceases to flow out of the outlet port, as all of the fluid being pumped in collects in the arm and is used to expand the arm instead of just flowing through it. This is what I meant by adding a "collection" term to the equation. This increasing capacity of the arm must be accounted for in a fluid balance.

 

[BigInch]

Cylinder4 is filled initially, when cylinder 3, 2, 1 are filling, they are also extending at the velocity of the fluid in the cylinder, so consequently no flow leaves from the system until the target distance is reached, at which time flow to the cylinders should be stopped or diverted.

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