Question

Mark which statements below are true, using the following In a classical fluid every molecule making up the fluid is subject to Newton's laws. In a continuum approximation of a large number of these particles we may think in terms of a small element of the continuum, containing those particles, being subject to Newton's laws. Thinking in terms of local conditions, the fluid elements follow a path with a tangent to the path given by the fluid velocity vector field, dr dx dy dz If this were air, we would think of this as wind velocity. We need the acceleration to employ Newton's second law alx,y,zt) dv dr which can be expressed explicitly with the chain rule. We will also use, P P& p, p, g, η, which represent the mass density, pressure, gravitational acceleration, and dynamic viscosity respectively After simplifying the acceleration and multiplying by the mass density, we get the force per unit volume. If we suppose this force originates from pressure differences, gravity, and internal friction then dv ar which is known as the Navier-Stokes equation. If the viscosity is ignored the resulting equation ไท ar gets a different name: the Euler equation. Fluids can be solenoidal so we define the vorticity. To a high approximation fluids also behave as being incompressible, which means that the mass density does not depend on time when only considering the flow

Based on the general definitions provided at the beginning, could someone please explain if the above statement A. holds true or false?

Answer 1

Gravitational potential is the scalar function F whose gradient is equal to opposite of gravitational field. i.e. g = -nabla phi rightarrow gravitation potential As we know gravitational potential is a conservative force. Conservative force rightarrow Path dependent. so nabla times g = nabla times (-nabla phi) = 0[As or a gradient is zero] so ans True