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An emergency supply system uses an accumulator pressurized at 100 bar to extend a cylinder. This has a piston diameter D = 15 cm and sees a force of 50 kN. The connection between the cylinder and the accumulator is managed through a normally closed solenoid valve. The valve, when energized, implements a restriction equivalent to an orifice (this feature is represented in the valve symbol) with diameter of 4.4 mm and flow coefficient of 0.7. Assuming the accumulator is large enough to maintain a constant supply pressure, calculate the cylinder extension speed. Elaborate a simple system modification (without changing any of the existing components) for reducing the extension velocity to 60% of the previous value. Assume the pressure of the accumulator constant during the cylinder extension.

Given:

The ISO schematic of the hydraulic emergency system, which includes an accumulator as energy source, an on/off valve, and a linear actuator. The upstream pressure of the accumulator, constant, p_acc = 100 bar; the orifice diameter d₀ = 4.4 mm and the flow coefficient C_f = 0.7. The load on the actuator is F = 50 kN and the piston diameter, D = 15 cm.

Find:

The extension velocity of the piston,