Bulk Modulus of Elasticity and Compressibility - Fluid Mechanics - Physics Practice Problems

TL;DR

When an object is submerged in a fluid, the fluid exerts pressure on the object, causing its volume to decrease. This change in volume can be calculated using the bulk modulus and pressure of the fluid.

Transcript

so let's say if we have a vessel filled with water and on the inside we have a sphere the fluid is going to exert a force on all directions on the surface of the sphere so all of these inward forces exert a pressure on this object so whenever you place an object in a fluid like water the volume of the object will decrease due to the internal forces... Read More

Key Insights

• 🙃 The volume of an object decreases when submerged in a fluid due to the pressure exerted by the fluid from all sides.
• 🔇 The change in volume can be calculated using the bulk modulus, pressure, and original volume of the object.
• 🫢 The compressibility of gases, liquids, and solids varies, with gases being highly compressible and solids being nearly incompressible.
• 😘 The bulk modulus represents the object's resistance to compression, with higher values indicating lower compressibility.
• 🔇 The bulk stress is equal to the pressure exerted by the fluid, while the bulk strain represents the fractional change in volume of the object.
• 🏑 Understanding pressure and volume changes in fluids is important in fields such as engineering, physics, and material science.
• 🔇 Different fluids may have different effects on the volume change of an object depending on their pressure and bulk modulus.

Questions & Answers

Q: How does the volume of an object change when it is submerged in a fluid?

When an object is submerged in a fluid, the fluid exerts pressure on all sides of the object, causing it to compress and decrease in volume.

Q: What is the relationship between the bulk modulus and volume change in a fluid?

The bulk modulus is a measure of the object's resistance to compression in a fluid. It is related to the change in volume by the equation: change in volume = -(pressure * original volume) / bulk modulus.

Q: How does the compressibility of gases, liquids, and solids differ?

Gases are highly compressible, meaning they can be easily compressed and have a low bulk modulus. Liquids have a moderate compressibility, while solids are nearly incompressible and have a high bulk modulus.

Q: How can the bulk stress and bulk strain of an object in a fluid be calculated?

Bulk stress, which is the force exerted by the fluid on the object divided by the area, is equal to the pressure exerted by the fluid. The bulk strain, which is the change in volume divided by the original volume, can be calculated by comparing the change in volume to the original volume.

Summary & Key Takeaways

• When an object is placed in a fluid, the fluid exerts pressure on all sides of the object, causing it to compress and decrease in volume.

• The change in volume can be calculated using the bulk modulus, which is a measure of the object's resistance to compression, and the pressure exerted by the fluid.

• The bulk modulus is related to the compressibility of the object, with gases being highly compressible, liquids being moderately compressible, and solids being nearly incompressible.