Control Volume Analysis Flashcards
What are the system equations applied to?
Fixed quantities of mass (or systems)
By name, what are the system equations
Conservation of Mass
Newton’s 2nd Law
Toeque Angular Momentum
Conservation of Energy
Conservation of mass equation
mass of a system is constant, dm/dt=0
Newton’s 2nd law equation
F=ma =d(mv)/dt
Torque Angular momentum equation
T= Iw(dot) = dU/dt
w(dot)=angular acceleration
U=angular momentum
Conservation of energy equation
Q-W = dE
When considering a fluid in motion, control volume analysis is used in which the system equations are rewritten to what…
Mass Continuity Equation, MCE
Force momentum equatio, FME
Torque angular momentum equation, TAME
Steady flow energy equation, SFEE
What porblems are solved via control volume analysis aka rewritten system equations (MCE, FME, TAME, SFEE)
- mass flow through a pipe network
- force on a pipe bend caused by fluid flow
- speed of rotation of a sprinkler
- power generated by water turbine
- power required by pump
In steady flow, the rate of change of momentum (dMcv/dt) = 0, what is FME reduced to
sumF=(sumM(dot)out - sumM(dot)in)
aka total force is the difference between the momentum flow rate out and in
In steady flow 1D incompressible flow, velocity at inlet/outlet is considered the same ie. M(dot)in=m(dot)in*Uin. what is the FME reduced to
sumF = m(dot)(Uout - Uin)
aka
net force is the mass flow rate * difference between velocities out and in
What variables must be considered for a control volume through a pipe?
velocity of the fluid in&out (u); pressure acting inwards (p); area of pipe (A)
how is momentum flow rate/flux caulculated? (M(dot))
M(dot) = m(dot) * u
mass flow rate * velocity
force of a fluid is given by
pressure * area
what is the FME equation
sumF= (sumM(dot)out - sumM(dot)in) + dM(dot)cv/dt
aka net force = (difference in net momentum flux) + rate of change of moment
what is the TAME equation
sumT = (sumO(dot)out - sumO(dot)in)
aka net Torque = (difference in net angular momentum flux)
