) As shown in Figure 10.9 a cylinder is completely filled with water and a force ? applied to the airtight movable piston which forms one end of the cylinder. What force will need to be applied to the piston for the volume of the cylinder to increase by 1 cubic millimetre (which equals 10−9 m3 )? (?water = 2.2 × 109 Pa) (b) If the cylinder was filled with air instead (?air = 1.42 × 105 Pa) what force would be required to increase the volume of air by 1 cubicmillimetre?
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
10.18 Refer to Figure 10.9 to answer the following questions:
(a) As shown in Figure 10.9 a cylinder is completely filled with water and a force ? applied to the airtight movable piston which forms one end of the cylinder. What force will need to be applied to the piston for the volume of the cylinder to increase by 1 cubic millimetre (which equals 10−9 m3 )? (?water = 2.2 × 109 Pa)
(b) If the cylinder was filled with air instead (?air = 1.42 × 105 Pa) what force would be required to increase the volume of air by 1 cubicmillimetre?
![### Figure 10.9 Explanation
This diagram illustrates a piston-cylinder apparatus filled with water. The diagram describes the following components and concepts:
- **Piston and Cylinder**: The piston is located at the top of the cylinder, and it can move up and down within the cylinder. The cylinder is filled with water, and the piston is used to apply force to the water inside.
- **Force (F)**: A force (indicated by a red arrow labeled F) is applied upwardly on the piston. This force acts over the area of the piston, which affects the pressure and subsequently changes the volume of the water.
- **Surface Area (A = 0.0314 m²)**: The cross-sectional area of the piston is given as 0.0314 square meters. This area is crucial for calculating the pressure applied by the force using the formula Pressure = Force/Area.
- **Initial Volume (V₀ = 0.5 L)**: The initial volume of the water inside the cylinder is 0.5 liters. This volume will change as the piston moves due to the applied force.
The diagram and accompanying text explain how applying a force to the piston changes the physical state of the water inside the cylinder by altering its volume. This setup can be used to demonstrate principles of fluid dynamics and pressure-volume relationships.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce3589f0-5608-4fb5-a11c-ce1805f2c8e6%2Fb06b6fcf-1f30-48d7-a6e2-e98658abc51c%2Fvi78nq_processed.png&w=3840&q=75)
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