A pneumatic system consists of several identical 1.5 inch diameter cylinders to lift 450-pound pallets in a warehouse. the gauge pressure in the system reservoir remains at 75 psi, and the atmospheric pressure is 14.7 psi. assuming that the weight of the pistons is negligible, determine the total number of 1.5-inch cylinders needed in the pneumatic system to lift the 450-pound load.

The applicable equation:

P = F/A

P = pressure

F = Force or weight

A = surface area

Pressure on each cylinder = (W/n) / A

Where n = number of cylinders. Additionally, pressure in the reservoir is equivalent to the pressure in each cylinder.

Net pressure = 75 - 14.7 = 60.3 psi

Therefore,

60.3 = (W/n) / A = (450/n) / (πD^2/4) = (450/n) / (π*1.5^2/4) = (450/n) / (1.7671)

60.3*1.7671 = 450/n

106.03 = 450/n

n = 450/106.3 = 4.244 ≈ 5

The number of cylinders is 5.