Give a detailed explanation of each of the two terms in the

Give a detailed explanation of each of the two terms in the equation for conservation of mass below and provide two real physical examples of each partial differential/partial differential t integral_cv rho dv + integral_cs rho v middot dA = 0 Why is it that there is a derivative in the first term with respect to time, and not in the second? Why do we integrate the first term over a control volume and the other over the control surface. Why is it that the expression is equal to zero for conservation of mass, but not for momentum, energy, etc.?

Solution

a. the first rem is rate of change of mass in the control volume whereas the second term is the rate of change of mass for control surface

b. in the first part control volume is taken , the density is constant and hence the derivative is with respect to time bcoz density * rate of change of volume will be rate of change of mass,whereas in second term volume flow rate is given as velocity * change in area therfore there is no need for time derivative. Just use simple dimension rule.

c. in first part overall volume is considered so integrate over control volume is needed,whereas in second term area is changing therefore integration over surface is taken

d. by dimension it is the conservation of mass only. since mass=density*rate of volume