What is the maximum line pressure in a system with a 35 hp motor, a 20 gpm pump, a cylinder diameter of 3 inches, and a safety factor of 6?

To determine the maximum line pressure in a hydraulics system, you can use the formula that incorporates the horsepower of the motor, the flow rate of the pump, the diameter of the cylinder, and a safety factor.

First, you need to calculate the force exerted by the hydraulic system. This can be achieved with the following steps:

1. Calculate the area of the cylinder: The area can be determined using the formula for the area of a circle, given by A = π(d/2)². With a diameter of 3 inches, the radius is 1.5 inches. Thus, the area A = π(1.5 in)² = π(2.25 in²) ≈ 7.07 in².

2. Convert horsepower to hydraulic pressure: The relationship between horsepower, flow rate, and pressure can be expressed with the formula:

[

\text{HP} = \frac{(P \times Q)}{33,000}

]

Where:

• HP is the horsepower (35 hp),

• P is the pressure in psi,

• Q is the flow rate in gallons per minute (20 gpm).

Rearranging