Exams › GATE › Technical

For a two-dimensional, incompressible flow having velocity components u and v in the x and y directions, respectively, the expression ∂(u²)/∂x + ∂(uv)/∂y can be simplified to

1. u ∂u/∂x + v ∂u/∂y
2. u ∂v/∂x + v ∂v/∂y
3. ∂u/∂x + ∂v/∂y
4. u ∂u/∂y + v ∂v/∂x

Correct answer: u ∂u/∂x + v ∂u/∂y

Solution

The correct option is derived from applying the product rule of differentiation to the terms u² and uv, leading to the simplification that expresses the change in kinetic energy per unit volume in terms of the velocity components and their gradients.

Related GATE Technical questions

• The size distribution of the powder particles used in Powder Metallurgy process can be determined by
• In a CNC machine tool, the function of an interpolator is to generate
• The machining process that involves thermal energy is
• The allowance provided in between a hole and a shaft is calculated from the difference between
• Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate?
• The controlling force curves P, Q and R for a spring controlled governor are shown in the figure, where r1 and r2 are any two radii of rotation.

⚔️ Practice GATE Technical free + battle 1v1 →