This questions deals with basics regarding the balance equations associated with

Question

This questions deals with basics regarding the balance equations associated with systems. Please give details.

a) what are the two general mass and energy balance equations, written in rate form, and when is it appropriate to use this form?

b)  What are the two general mass and energy balance equations, written in magnitude (finite difference)
form and assuming uniform flow, and when is it appropriate to use this form?

c) Assume a stationary system, appropriately modify the balance equations from a) and b).

d)  If the system is closed, appropriately modify the balance equations from b).

e) Assume steady-flow, appropriately modify the balance equations from a).

f) Assume adiabatic conditions and only a moving boundary, appropriately modify the balance equations
from b).

Explanation / Answer

A)

energy: dEcv/dt=Qdot net in+Wdot net in+mdot in*theta in - mdot out* theta out, where theta=(1/2)v^2+gz+h

mass: dMcv/dt= mdot in - mdot out

rate form= continious ( no finite ending). Ex) steady flow device

B)

finite time(cycle). definite start and end

E2=E1+Qnetin+wnetin+m in*thetain-mout*thetaout

m2-m1=sigma min+ sigma mout

C)

stationary= NO delta KE or PE

theta=(1/2)v^2+gz+h

KE & PE= theta

dEcv/dt=Qdot in+Wdot in+mdot in*theta in - mdot out* theta out

dE/dt=0

Qin=-Qout :answer

dMcv/dt=mdotin-mdotout

0=mdot1-mdot2 or mdot1=mdot2=mdot

dMcv/dt= mdot in - mdot out

E2-E1=-Wnetin+min*thetain

m2-m2=min

D)

doesnt depend on open/closed system!

same as B ans

E)

Dmcv/dt= Min-mout

0=m1-m2

m1=m2=m ans

F)

E2=E1+wnetin+mneti*thetanetin-mnetout*thetanetout

deta E= -Wb+min*theta in (theta goes away bc its uniform)

U2-U1=-Wb+min ans

m2-m1=sigma min- sigma mout

m2-m2= min ANS

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