Question

What is the dynamic equation for non-uniform flow ? How is it derived!

Answer 1

[AI-generated answer — Bot GPT 3.5]

The dynamic equation for non-uniform flow is the momentum equation, which is derived from the application of Newton's second law of motion to a fluid element. In the momentum equation, the forces acting on a fluid element - including pressure forces, gravity forces, and viscous forces - are balanced by the rate of change of momentum within the fluid element.

The momentum equation for non-uniform flow can be derived by considering a control volume within a fluid flow field. The momentum equation is then obtained by applying the conservation of linear momentum to the control volume, taking into account the forces acting on the fluid element and the rate of change of momentum within the control volume.

The momentum equation for non-uniform flow can be written in vector form as:

∂(ρv)/∂t + ∇(ρv⋅v) = -∇P + ρg + ∇⋅τ

where:
- ρ is the density of the fluid,
- v is the velocity vector of the fluid element,
- t is time,
- P is the pressure,
- g is the gravitational acceleration vector,
- τ is the viscous stress tensor,
- ∇ is the nabla operator, and
- ∂/∂t represents the partial derivative with respect to time.

This momentum equation describes how the fluid velocity changes in response to the various forces acting on it in a non-uniform flow field. By solving the momentum equation, the velocity distribution and flow behavior of a non-uniform flow can be analyzed and predicted.