Question

Which one of the following is the Poisson’s ratio for an incompressible fluid?

• A. 0
• B. 0.25
• C. 1
• D. 0.5

Hint:

For incompressible fluids, Poisson's ratio is always 0.5, as the material undergoes equal lateral and longitudinal strains to maintain constant volume.

Answer 1

The Correct Option is D

Poisson's ratio, \( \nu \), is a material constant that relates the longitudinal strain to the lateral strain when a material is subjected to uniaxial stress. It is defined as: \[ \nu = -\frac{\text{lateral strain}}{\text{longitudinal strain}}. \] For most materials, when subjected to stretching or compression, the material experiences both a change in length (longitudinal strain) and a change in width (lateral strain). For an incompressible fluid, the volume of the fluid does not change when subjected to pressure, which means that any change in length is accompanied by an equal change in width in such a way that the volume remains constant. Step 1: Incompressible Fluid
Incompressibility implies that the bulk modulus of the fluid is infinite, meaning the volume does not change under pressure. For such fluids, the relationship between the longitudinal strain and the lateral strain results in Poisson’s ratio being exactly 0.5. This is because the lateral strain must be equal to the longitudinal strain to maintain constant volume. Step 2: Poisson’s Ratio for Incompressible Fluids
For an incompressible material, Poisson’s ratio reaches its maximum value of 0.5. This means that for every unit of longitudinal deformation, there will be an equal amount of lateral deformation, thus ensuring that the material’s volume does not change. Step 3: Conclusion
Hence, for an incompressible fluid, Poisson’s ratio is 0.5. Therefore, the correct answer is (D) 0.5. Thus, the correct answer is (D) 0.5.