A valve in the cylinder shown in Fig. P 2.47 has a cross-sectional area of 11 cm^2 with a pressu

step 1 So in this problem, we want to find the force needed to open this valve on a cylinder. So what w

A valve in the cylinder shown in Fig. P 2.47 has a...

A valve in the cylinder shown in Fig. $\mathrm{P} 2.47$ has a cross-sectional area of $11 \mathrm{cm}^{2}$ with a pressure of $735 \mathrm{kPa}$ inside the cylinder and $99 \mathrm{kPa}$ outside. How large a force is needed to open the valve?

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Key Concepts

Pressure

Pressure is defined as the force exerted per unit area and is a fundamental concept in fluid mechanics. It helps quantify how much force is distributed over a given area and is essential in understanding how fluids behave under different conditions.

Area

Area refers to the surface over which a force or pressure is applied. In the context of fluid mechanics, the cross-sectional area where a pressure is applied determines the magnitude of the total force transmitted through the fluid.

Pressure Differential

The pressure differential is the difference between the pressures on two sides of a surface. This difference is crucial because it creates a net force that can cause movement or mechanical action, such as opening a valve.

Force Calculation from Pressure Difference

The force exerted by a pressure difference across an area is calculated using the formula F = ?P × A, where ?P is the pressure differential and A is the cross-sectional area. This principle is widely used in analyzing hydraulic and pneumatic systems.

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