The -tall cylinder in FIGURE P14.61 contains air at a pressure of . A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from escaping, then mercury is slowly poured into the cylinder until no more can be added without the cylinder overflowing. What is the height h of the column of compressed air?
Hint: Boyle's law, which you learned in chemistry, says for a gas compressed at constant temperature, which we will assume to be the case.
Hence, the length of air column is
The force applied perpendicular to an object's surface per unit area across which that force is spread is known as pressure. The pressure gauged in relation to the ambient pressure is known as gauge pressure. Pressure is measured in a variety of ways. The perpendicular force per unit area, or the tension at a point within a confined fluid, is known as pressure in the physical sciences.
An ideal gas obeys Boyle's law. The Boyle's law states that the product of pressure and volume is constant for constant temperature condition. The Boyle's law expression is:
The initial pressure and volume in the column are and . The area of cross section of the cylinder is . The length of the cylinder is . The length of the air column is . The air column will obey Boyle's law.
The final pressure is
The final volume is
Apply Boyle's law to the column of gas:
An aquarium of length , width (front to back) , and depth is filled to the top with liquid of density
a. Find an expression for the force of the liquid on the bottom of the aquarium.
b. Find an expression for the force of the liquid on the front window of the aquarium.
c. Evaluate the forces for a-long, deep aquarium filled with water.
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