Question

The y-momentum equation falls into which of these types of PDEs?

(a) 1-D first order equation

(b) 2-D second order equation

(c) 2-D first order equation

(d) 1-D first order equation

The question was asked by my school teacher while I was bunking the class.

I'm obligated to ask this question of Partial Differential Equation in division Mathematical Behaviour of Partial Differential Equations of Computational Fluid Dynamics

Answer 1

The correct option is (b) 2-D second order equation

To elaborate: The y-momentum equation is

\(\frac{\partial (\rho u)}{\partial t}+\frac{\partial (\rho u^2 )}{\partial x}+\frac{\partial (\rho uv)}{\partial y}=-\frac{\partial p}{\partial x}+\frac{\partial}{\partial x}[(\nabla.\vec{V})+2\mu\frac{\partial u}{\partial x}]+\frac{\partial}{\partial y}[\mu(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x})]+\rho f_x\)

When expanded it gets second derivatives and hence it is a second order equation of x and y dimensions.