A piston/cylinder with a cross-sectional area of 0.1 ft^2 has a piston mass of 200 lbm resting o

step 1 So in order to find what the water pressure should be in a cylinder that's covered by a piston,

A piston/cylinder with a cross-sectional area of 0.1 ft^2...

A piston/cylinder with a cross-sectional area of $0.1 \mathrm{ft}^{2}$ has a piston mass of 200 lbm resting on the stops, as shown in Fig. $\mathrm{P} 1.50 .$ With an outside atmospheric pressure of 1 atm, what should the water pressure be to lift the piston?

Key Concepts

Gauge and Absolute Pressure

Gauge pressure is the pressure measurement relative to the ambient atmospheric pressure, while absolute pressure includes the atmospheric pressure in its measurement. In many applications, especially involving hydraulic and pneumatic systems, it is important to distinguish between these two measurements, as the external pressure (like atmospheric pressure) impacts the net force acting on system components.

Pressure

Pressure is defined as the force exerted per unit area. In many engineering applications, this relationship is used to calculate how a force distributed over an area results in a pressure, measured in units like Pascals or psi. In hydraulic systems, an increase in pressure corresponds directly to an increase in the force generated at the area of a piston or diaphragm.

Force Calculation

Force is the product of mass and gravitational acceleration; in mechanical systems, this allows the conversion of a given mass into a weight (or force) which needs to be balanced by other forces. This concept is essential for determining the necessary input force in systems such as hydraulic lifts where a known load must be raised or balanced.

Static Equilibrium

Static equilibrium refers to the state of a system when the net force and net moment acting on it are zero, meaning the system is at rest or moving at a constant velocity. Analyzing static equilibrium conditions is crucial in determining the balance of forces in mechanical systems, ensuring that the input forces (like hydraulic pressure) match the resisting forces (such as weight and atmospheric pressure).

Hydraulic Lift Principles

Hydraulic lift systems operate on the principle that pressure applied to a confined fluid is transmitted equally in all directions. This principle enables a relatively small pressure applied over a small area to generate a large force on a larger area, making hydraulic systems effective for lifting heavy loads. Understanding this concept is key to designing and analyzing systems where fluid pressure is used to move or support objects.

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