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FAQs on Unit-5: Relation between shear stress, pressure gradient and velocity distribution - Lecture Notes - JEE
| 1. What is shear stress and how is it related to pressure gradient and velocity distribution? |  |
Ans. Shear stress is a measure of the force per unit area that is exerted parallel to the surface of an object or fluid. It is related to the pressure gradient and velocity distribution through the concept of viscosity. Viscosity is a measure of a fluid's resistance to flow, and it determines the rate at which shear stress is generated. In a fluid with a high viscosity, shear stress is generated more easily for a given pressure gradient and velocity distribution, while in a fluid with low viscosity, shear stress is generated less easily.
| 2. How does pressure gradient affect shear stress and velocity distribution? | |
Ans. The pressure gradient plays a crucial role in determining the shear stress and velocity distribution in a fluid. A high pressure gradient results in a larger difference in pressure between two points in the fluid, which in turn leads to a higher shear stress. This higher shear stress causes the fluid particles to move faster, resulting in a higher velocity distribution. Conversely, a low pressure gradient leads to a smaller difference in pressure and lower shear stress, resulting in a slower velocity distribution.
| 3. What is the significance of velocity distribution in relation to shear stress and pressure gradient? | |
Ans. Velocity distribution refers to how the velocity of a fluid varies across its cross-section. It is significant because it directly affects the shear stress and pressure gradient. In a fluid with a uniform velocity distribution, the shear stress is constant throughout the fluid, and the pressure gradient is zero. However, in a fluid with a non-uniform velocity distribution, there are variations in shear stress and pressure gradient. Higher velocity gradients result in higher shear stress and pressure gradients, while lower velocity gradients result in lower shear stress and pressure gradients.
| 4. How does the viscosity of a fluid impact the relation between shear stress, pressure gradient, and velocity distribution? | |
Ans. The viscosity of a fluid determines how easily it deforms under the influence of shear stress. A fluid with high viscosity resists deformation more, resulting in a higher shear stress for a given pressure gradient and velocity distribution. On the other hand, a fluid with low viscosity deforms more easily, leading to a lower shear stress. Therefore, the viscosity of a fluid directly influences the relation between shear stress, pressure gradient, and velocity distribution.
| 5. How can the relation between shear stress, pressure gradient, and velocity distribution be explained using real-life examples? | |
Ans. The relation between shear stress, pressure gradient, and velocity distribution can be understood through various real-life examples. For instance, when you pour honey from a jar, it flows slowly due to its high viscosity. The pressure gradient between the top and bottom of the jar is small, resulting in a low shear stress and slow velocity distribution. On the other hand, when you pour water from a tap, it flows quickly due to its low viscosity. The pressure gradient is higher, leading to a higher shear stress and fast velocity distribution. These examples demonstrate how the properties of a fluid and the pressure gradient affect the shear stress and velocity distribution.
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