Final answer:
The flow rate coming out of the cap end of the cylinder with a 3.5" bore and a 3/4" rod is 166.28 GPM, calculated by the difference in area between the cap end and the rod end.
Step-by-step explanation:
To determine the flow rate coming out of the cap end of the cylinder, we need to consider the volume displaced by the rod when the cylinder retracts. Since fluid is incompressible, the cylinder displacement minus the rod volume equals the volume output at the cap end.
First, we calculate the rod and bore areas using the formula for the area of a circle, A = π(d/2)^2, where π is approximately 3.14159265359.
Cap (bore) area:
Acap = π(3.5/2)^2 = 9.621 in2
Rod area:
Arod = π(0.75/2)^2 = 0.4418 in2
The net area when the cylinder retracts is the difference between the two:
Anet = Acap - Arod = 9.621 - 0.4418 = 9.1792 in2
Next, to find the flow rate in GPM from the cap end, we take into account that the flow rate Q is the product of the area A and velocity v, and we have flow in GPM:
Qcap = (Anet / Arod) * Qrod
Qcap = (9.1792 in2 / 0.4418 in2) * 8 GPM
Qcap ≈ 166.28 GPM
The flow rate coming out of the cap end of the cylinder is approximately 166.28 GPM, assuming that the flow into the rod side is 8 GPM and the rod displaces its own volume of fluid.