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mechanics Cheat Sheet (DRAFT) by

this cheat sheet covers balance equations and stress

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Linear momentum - mass system

Reynold's Theorem: the bridge. Mass system to control volume. Lagrang to Eulerian
if t=t: Bsys=Bcv, CV=Sys, occupy the same space
extensive quatities (B): depend on the size of the region. If 𝐵 = 𝑚 then b = 1 If 𝐵 = 𝑚𝑣 then b = 𝑣
if t=t +∆t, Bsys≠ Bcv, Cv≠Sys, we use Reynolds here.
intensive quantities (b): indepe­ndent of the size
Flow rate: Q=Av, if p is consta­nt→mass flow rate

Reynolds formula

when a moving CV we have w as the relative velocity. w= vb-vcs1
  

Forces acting on fluids

dP/dt=­ΣFs­ys=­ΣFcv, where P=mv:m­omentum
  

How to set up a cv problem

whats happening, whats gonna cause. What are we trying to solve.
To draw CV: we think of where you bisert­s-cut into 2 parts
In volume: be within the boundaries of CV. Area integral: must bisect the bounda­rie­s/s­urface of CV
Accumm­ula­tion? In which integral are we looking. Does the quality act on the surface. Align the flow with dirt vector,
 

mass vs linear momentum

Balance of Mass: Finding flow rates, the relati­onship velocities and areas. Scalar. (-/+) from scalar product
Balance of Linear Momentum: Finding relatshs btnw flow properties and forces. Vector. (-/+) from scalar product or direct of vector quantities
B of mass in B of linear momentum problems to find unknown.