ch. 6 open systems

open systems / control volume

open systems

mass and energy allowed to cross the boundaries at any point

control volume

• shape is fixed

• energy and mass allowed to flow

control mass

• no mass allowed in and out

• energy allowed to move across boundary

• shape is allowed to change

mass flow rate expressions

• m’ = ρ • A • v = density x area x velocity

• m’ = 1/v • A • v = (area x velocity) / specific volume

conservation of mass in control volume

the amount of mass in = the amount of mass out of the open system

conservation of mass expression

(mass entering the control volume ) - (mass exiting the control volume ) = ( change in the mass of the control volume)

conservation of mass formula

∑ Mi - ∑ Me = ∆ M c.v.

conservation of mass formula in rate form

• process ongoing continuously

• ∑ m’ i - ∑ m’ e = ∆m / ∆t = dMc.v. / dt

steady state conditions

• constant with time

• derivative goes to 0 because it no longer changes with time

conservation of mass steady state expression

∑ m’i - ∑m’e = 0 —> ∑m’i = ∑m’e

flow work / flow energy definition

• similar idea to boundary work in closed system

• the new mass displaces the control volume upon entrance an exit so it does work

flow work expression

∫ F • ds = F • ds = P • A • s = P • V

first law per unit mass expression

qin + win + pi • vi + ui + ½ v²i + gzi -qout - wout - pe • ve + ue +1/2 v²e + gze = ∆e c.v.

for total mass

Qin + Win + mi ( hi + ½ vi² + gzi) - Qout - Wout - me (he +1/2 ve² +gze) = ∆ E c.v.

per unit time / rate form

Q’net + W’net + mi(hi ½ v² +gzi) + me(he + ½ ve² +gze) = ∆Ec.v. = dEc.v. / dt

steady state condition

• same constant at all times

• derivative = 0

• mass in = mass out

• will be used most of the time for open systems

steady state condition equation

Q’net - W’net + mi(hi + ½ vi² + gzi) - me (he + ½ ve² + gze) = 0