Lecture 3 Flashcards
(13 cards)
How is the mass flow rate in and out of a system written WRT x-direction? How does this change for other directions?
dxdz for in, and dx)dydz changes for other directions
How do you calculate net mass flow rate for the x-direction? What is the equation for this in the continuity equation?
Net = out - in
Mass in element = rho * volume , where dxdydz is volume
What’s the equation for net mass flow rate out for all directions?
Sum of net flow for all directions
Rate of mass increase through system equation?
How do you get to the continuity equation?
Net flow out = Net mass decrease
Tensor notation for continuity equation
What is the divergence operator?
What does it mean if the divergence form of the continuity equation is greater than 0?
The system is expanding; if < 0, it’s contracting.
What is the divergence form of the continuity equation also known as?
Vector form
What is the LAGRANGIAN form of the continuity equation?
What does the total derivative expand into?
What are the definitions of substantial (total), local, and convective derivatives?
Total: rate of change of time following a moving fluid element
Local: rate of change of time at fixed point
Convective: rate of change of time due to movement of the fluid
What is the symbol for local and convective derivatives?
Local: ∂/∂t
Convective: u(∂/∂x)+v(∂/∂y)+w(∂/∂z)
